good evening my dear J Lions welcome AB to the roar series and ready to Roar for the first chapter of 12th standard which is electrostatics and gos law if you look at heta they have divided this chapter into two parts the first part being electrostatics field and potential where you basically talk about point charges and system of charges and even dipoles for that matter and find out the fields the energies the force and the you know potentials due to these system of charges or point charges so that is what we will be dealing in today's lecture there will be a separate class completely meant for gos law its applications and different geometries like shells sheets spheres conductor properties and so on and so forth all right so this this chapter into two Parts this is the first part of it I hope you are ready to Roar my dear lions and uh good evening kishori Dakar yesan headshot yoga ache good evening good evening good evening uh definitely definitely yep okay let's begin with the class and uh I hope you uh have smashed the like button in case you haven't done that Mark your attendance quickly even if you're watching it recorded because that is your small token of Guru dsha towards this lecture which are absolutely free of cost in English for all the J 25 and 26 aspirants so make sure you do that right away right now yep and subscribe to the channel so that you do not miss any of my classes on YouTube out here good evening good evening Psy good evening her neat aspirant also can watch this but slightly some questions will be of higher level hello adika good evening everyone hello yashwant yes so let's start with Electro stat IC what is um this chapter going to deal with probably some of you might be very new also to this chapter or it might have just started in your school or college see my dear students um you might have definitely played with Bits of Paper by rubbing on your friend's head and those pieces of paper get attracted so there is a magical force between those bits and pieces of paper and the scale which you are rubbed on somebody's head that Magical Force is called as the electric force and that electric force comes because of something called as charges and these charges are basically of two types one is positive one is negative the positive charge comes because of the protons which are there you know in that object all right excess protons and then the negative charge comes because of the electrons which are there in that particular object in fact in excess so these positive and negative elements you know play a very important role in creating electrical attraction and repulsion between any two bodies and that is what this particular topic or unit is going to deal with if you see the word electrostatics Electro is basically something got to do with that charge which creates that attraction and repulsion around it like the bits and pieces of paper you might have also seen that when you touch a door knob or Shake somebody's hand on a carpet you get a shock that shock is again got to do with this particular unit of electrostatics static because it is at rest or very low speed so in this chapter you will see the charges are almost like at rest or in equilibrium or at very low speeds and you are going to deal with such systems the next chapter after gos law is actually current electricity which can also be named as electrodynamics Electro charge Dynamics means in motion so charges under motion that happens in a wire which carries current when you have your electrical wires which light up your bulb fan AC TV Etc the charges are flowing through the wires so those charges under motion you study it under current electricity I hope this distinction is absolutely clear yep yes yes yes yesan this lecture plus 100 plus problems is good enough for this particular chapter just follow the uh you know routine which I gave you in yesterday's lecture the road map and the strategy for 99.99 percentile just check that out okay it's there in the past session you can see it uh in yesterday's part so this particular electric charge which creates that notion which creates that notion of electric force around it so this electrical charge creates creates something called as a field creates a field and can attract and it can basically attract or it can repel repel other charges can attract or repel other charges okay it can attract or repel other charges around it there are two kinds of charges which are found in nature one is basically the positive charge one is basically the positive charge and it is basically because of the protons present inside any atom the second type is the negative charge which is because of the electrons which are present in any atom you also have a third category which is not positive not negative basically it is neutral basically it is neutral it does not have only any charge so it is a neutral thing and that is because of let's say example neutrons it is neither positive nor negative it will neither attract nor will it repel any other charg particle hello Prav hello AI gaming yep so don't ask such questions how many questions will come from this chapter you just have to study if I tell you five questions what will you do if I tell you one question what will you do you'll still study the same chapter in the same uh you know enthusiasm and the same you know whatever hard work that you're going to put in just because one question is being asked will you study less at this point of time obviously you are not in the in a in a batch where you know you just have to complete the entire syllabus in one month you have good almost like s to 8 months make sure that you study every chapter in detail stop asking such questions I don't even make such videos where this chapter is only important this chapter is not important at this point of time you have to study everything please mind it okay so the neutrons n is basically neither going to attract nor is it going to repel anything so that is what you know electric charges are now you will also see now you'll also see just one second yep you'll also see like charges will always repel so like positive positive will always repel whereas unlike charges will always attract whereas unlike charges will always attract so in this particular scenario you will see there will be some kind of a repulsion so like charges like charges always end up repelling each other whereas opposite charges whereas opposite charges they will always attract so opposites Opposites Attract Opposites Attract and you would have seen this in your school and college also two people you know whom you know that this person thinks like this this person thinks completely off and they two are best friends or they two are very very good friends and you wonder how come these two people are very good friends so you know Opposites Attract and sometimes you see two people of the very same thinking or like two Toppers both of them are Toppers maybe they are not good friends with each other all right or two villains not good friends with each other all right so that is how it works probably in even in real life so Opposites Attract and like charges will repel remember this phrase that a neutral charge a neutral charge charge doesn't exert any Force doesn't experience doesn't experience or exal any Force doesn't exalt or experience any kind of force that is standard stand next important thing about electrical charges next important thing about the electrical charges which is found is that these charges are always found to be in multiples of something like for example we know that in our uh you know economy right probably we have one rupee coins these days we don't get Pisces long time back we used to get pises so you have a one rupee coin right uh maybe imagine after a few more years that one rupee coin is also gone 5 rupee coin is gone 2 rupee coin is gone you only have 10 rupee notes imagine you have only 10 rupe notes so if you want to trade if you want to buy something if you want to sell something you can only keep the cost of your item or you can only buy an item if it is like in multiples of 10 so for example it can be 200 rupees or it can be 150 rupees or it can be 2, 100 rupees or it can be 5 lakh uh rupees or 500 rupees these are all fine or even 30 Rupees is fine but what I cannot have what I cannot have is 15 rupees or 26 rupees or you know 2.5 rupees or you know 100.2 rupees or let's say 5 six rupees all these are impossible to achieve using the 10 rupe notes this is our smallest denomination also called as the quanta of money this is also called as the quanta quantum quanta quanta is a small part quanta of money which is possible and every other money that I have is a multiple of this 10 Rupees hence I would say the money is quantized the money is quantized this is quanta everything is multiple of this so it is quantized similarly you will see in nature charge is also quantized you cannot write any random charge it is not going to really happen only if it is a multiple of a certain value and what is that certain value well it is 1.6 1.6 into 10 ^ -9 whether you take positive or negative doesn't matter is the smallest charge possible is the smallest charge possible is the smallest charge possible and every other charge any charge any charge any charge is basically some integral multiples of this particular value which is 1.6 into 10 ^ -19 actually that 1.6 into 10^ minus 19 is also called as e is also called as e basically the charge of an electron so this is a very very important uh thing here basically n can be any integer here n is basically any integer positive or negative and the value of e and the value of e is 1.6 10^ -19 kums 1.6 10 the^ -9 kums which also brings me to the idea what is the unit of charge what is the unit what is the unit of charge the unit of charge in SI system is basically Kum is basically Kum symbol for that is C if I talk about the dimension if I talk about the dimensions of uh the charge well it is ampere into time it is ampere ra to 1 time ra to 1 remember it is not a fundamental unit it is a derived unit or derived quantity it is a derived derived quantity it is not a fundamental quantity current is a fundamental quantity current into time is kums current into time is basically the kums part okay I hope this much is clear I hope this much is clear yeah yes very good so all these things you should definitely definitely know now the next important thing the next important thing which you should know know is that you cannot you cannot create a new charge or nor can you get rid of any charge you will see no matter what happens the total charge in this universe remains conserved not just that if you take an isolated system isolated mean nothing can go out nothing can come in just like your classroom when your teacher is inside and specifically if your teacher is very very strict nobody can exit the classroom for a l bre nor can you go out for drinking water nor can you go out to get something nor can somebody who is late enter the classroom so that classroom with a strict teacher becomes an isolated classroom until the Bell Rings nobody can go in or out so same way if I have an isolated system no charge can go out no charge can come in whatever happens within the system stays intact so you will see the total charge remains conserved in an isolated system very very important so this is total charge total charge remains total charge remains conserved remains conserved in an isolated system in an isolated system there can be many examples of this imagine I have a neutral body imagine I have a neutral body and let's say I break it into two parts I break it into two parts and let's say this one acquires three positive charges over it naturally to conserve the total charge there must be three negative charges on this body it has to happen because the total charge on this was Zero the total final charge must be zero you can see the charge is conserved same way imagine this imagine this there is one body here okay and let's say another okay and another body over here I rub them and then I see what are the final charges on both the bodies let's say for example this had one positive charge and let's say this had you know some three or four negative charges let's say three negative charges I rub them something happens some exchange happens and finally they acquire some charges if you count the total charge of the system one positive three negative three negatives one positive make get two negative so the total charge of the system is two negative charges which means which means by some reason or some way just imagine something happens over here this becomes two positive over here this has let's say you know uh let's say for example one negative over here then to conserve the charge to conserve the charge I need to to make sure the total charge is two negative right now there are two positives one negative it is + one so I need to add more 1 2 and three negatives just check this out what has happened over here what has happened over here now the total charge is basically conserved 1 2 3 negatives + one will make it min-2 1 2 3 four negatives plus two will still make it -2 so this is okay this is basically okay there is nothing wrong with this diagram all right everyone understood till this point everybody understood it till this point so you have to basically conserve the total charge of the system to conserve the total charge of the system correct very good so total charge is conserved so this is the principle of charge conservation this is the principle of charge conservation charge conservation keep this in mind the other one over here this was the principle of quantization this was the principle of quantization okay this was a principle of quantization all these are very very important things and I think I have put it down as a summary point also over here electric charge is a fundamental means it's a very Elementary property anything into existence will have either positive negative or zero charge anything which has mass all right you'll see that protons neutrons all these things they have mass they also have charge some have no charge some have positive some have negative positive positive negative negative will repel positive with negative basically unlike will attract okay and charge is quantized and charge is also conserved also one more thing just because you move a charge here and there does not mean the charge will change it will still remain the same uh you don't have to know so much about it right now but just keep in mind that when you move a mass really fast the mass value changes using relativity principles but charge is not like that just because you move a charge really fast does not mean the charge will change okay mass does change okay when you move a mass really really fast closer to the speeds of light but charge there is nothing like that it is relativ uh relativistically speaking it is invariant okay so J wise this is not important at all but just giving you an additional piece of information so I think let's start with some questions coming up on your screen how many electrons are there in 16 micrum of charge 16 micrum of charge let's think about it so we know that the total charge is always n * of e the total charge is 16 micro micro is 10 10^ - 6 n value I do not know e value is 1.6 into 10^ - 19 which I can also write it as 16 into 10^ minus 20 right now you will see that this particular 16 and this particular 16 will get cancelled will get cancelled therefore this n will be 10 ^ - 6 is on the top and this 10 the^ - 20 is below therefore the value of n will become take 20 on the top it will become 10 the^ 14 so 10 the power 14 electrons are there in um you know in this particular amount of charge actually the charge should have been mentioned as negative then it is okay or else you know electrons won't be there in positive charge yes 10 to the^ 14 perfect perfect amazing amazing okay moving on to the next question if a body is rubbed with another identical body if a body is rubbed with any other identical body A and B are the same looking bodies and it is found that a becomes positively charged as compared to B then compare the masses of A and B who do you think will have higher Mass so you have a body a and you have a body B A and B are identical but earlier they were neutral after you rub them after you rub them them you know this becomes let's say positively charged obviously an equal amount of negative charge will develop over here so the question is who has more mass Now understand this when I say a body is neutral it could mean it has only neutrons or it has equal number of protons and electrons now usually most of our bodies are made of atoms so obviously it has protons and electrons in those atoms so an atom when I say is electrically neutral basically number of protons and number of electrons are equal but when I say a body is positively charged that means that some of the electrons have left them imagine an atom and the electrons leave so there will be excess of protons basically positive charge if the electrons are acquired by some atom there will be excess electrons so that atom will become negative and that body will also become negative it means that electrons have jumped from here to here and even electrons have mass even electrons have mass so that's why this mass will be more whereas these electrons left them that's why the mass over here will be less because few of the electrons will leave so guys what will be the answer B's mass will be more than the mass of a B's mass will be more than the mass of a is that clear very few people answered it I can see adika answering it very good sha yes okay pay very good yes Dakar answer is not B it is basically c b will have more mass because though tiny meany electrons also have some teeny meany Mass so there will be a marginal Mass difference do not expect in grams or even milligrams it will be very very very very minute difference but yes that is what the question paper Setter wants to check your knowledge and your concept C okay so that's why we have to go with the flow very good very good sanana you have got admission in manipal College of Phat pharmaceutical Sciences I hope you like the branch and I hope you do really well in the branch and you you know really really study well very glad sanana happy for you if you are if you are interested in farmaceutical sciences and you want to make a career very good I really happy that you finally got a good college and you're excited for it very good if a repels b b attracts c c repels D then multiple options may be correct which of the following are correct this is the next level question level two let's see if you guys can solve this okay if a repels B so let's assume okay let's take the charges a b c and d only one of these options are possible a is positive or A is basically negative if a is positive a repels B that means this is also positive or this is also negative B attracts C that means C is negative or C is positive if this is negative this is positive C repels D that means C and D are like charges so it will be something like this so these are the only two possibilities this is case one this is basically your case two these are the only two cases now solve and check which of the options are correct now solve and check which of the following options are correct my dear students check this out come on first of all A and C are oppositely charged A and C A and C are oppositely charged definitely correct B and D are oppositely charged B and D B and D oppositely charged perfectly correct a and D are oppositely charged A and D A and D oppositely charged perfect C and D are like charges c d c d yes like charges so I think all of them are correct yes complete green a b c d all the options are correct definitely definitely okay all the options are correct some of you said only AB or ABD some only one who was that Kish very good very good Luffy very good mesu awesome awesome awesome yes all of them are actually correct okay so if you take cases and solve it no it becomes very easy for you to visualize or else you'll be only confused just looking at it so always the trick is to write in the rough work to solve in the rough work only then you will get it if you just mentally visualize you will lose track of what you are thinking one second's back and that is how you make silly mistakes in the exam moving to the next part and that is kulan's law that is the main part of this chapter and you will see all subsequent things are derived from this so my dear students imagine I tell you you know uh any two charges positive negative whatever will attract and repel each other but how much they attract how much they repel depends on their distance and also their charges this sounds very similar to what you might have studied in 11th standard in the chapter of gravitation remember two masses will always attract and how much is that attraction depends on how far they are and what is their masses same way you will say electrical force also depends in a very similar M and you will see even the formulas are very similar if you remember gravitational uh force of attraction Newton's law of gravity which was G M1 M2 by the distance Square you will see ELC force is also very similar some constant into q1 Q2 by r² it's very very similar so it feels as if Kum copied from Newton and acted very very cool about it yep both these formulas look very similar but the major difference between gravity and electrical force is can somebody tell me what is a major major differences one let me put gravitational force over here versus versus Kum force or electric force versus electric force what are the major major differences that you can find my dear students what are the major major differences that you can find gravitational force is only attractive gravitational force is only attractive whereas electric force can be attractive can be repulsive also so both are possible attraction repulsion both are possible yep are all these forces non-con yes yes all these forces are non-c cont forces meaning they do not physically touch you do not have to touch two masses together Wireless all these forces are Wi-Fi it's not like your wired USB connection only then the data transfer will happen it's like Wi-Fi antenas and they can communicate with each other why wirelessly and they can attract and Riel only and communicate via something called as field okay field is something which you cannot see which you cannot you know uh put it like a diagram in your charts or your books it's there and you can only feel it when you put a mass or put a charge another important thing is gravitational force is a very long range Force very very long range like Earth and Moon how far they are still they will attract Force there are tidal effects all the planets are going around the sun because of the gravitational force of the sun on all the other planets but you will see the electrons are going in the nucleus inside an atom because of the electric force which is present at a short distance it's not like I am getting attracted by some other electric charge there and I will have to get pulled by it no it's a very short distance Force so it's a very very short range force it is a very short range Force but the interesting thing is when your distances are very close then the electric force will dominate too much and it is much much stronger in that range so in that short range electric force is a very very strong force it is very very strong force in nature whereas you will see even gravity even gravity you know at that particular point of time becomes very very weak very very important is that clear okay so these are some basic things which you should know regarding gravitational and electrical forces okay so gravity is also considered as a weak force it is considered as a very very weak force great great uh Nila this is onot Marathon Yep this is one shot Marathon okay okay now we'll see the formula so the value of proportionality constant will differ yes that you can put it for the sake of it this is G over here here you will have K okay you can put that and it is because of charges here it is because of masses masses are the cause are the cause of the gravitation masses are the cause of the gravitation here you can say charges are the cause of charges are the cause of electric force charges are the cause of the electric force that's the main difference between the two so according to the kum's law he says that whenever you have two charges the force between them is inversely proportional to the square of the distance and directly proportional to the product of the charges that is why it is also called as the inverse Square law sometimes it is also called as the inverse inverse Square inverse Square law because the force between them because the force between them is proportional to the product of the charges and inversely proportional to the square of the distance between them that is how it is also keep in mind if one of the charges one of the charges small 5 Kum 1um 10um 1.6 Kum like that so tell me who will exert more force will fub1 be more or will F2 be more imagine this is like 20 30 kums this like one two kums like that who will be more F1 will be more or F2 will be more put it up in the chat box yep uh kishor who said that it is non Universal it is universal kishori yeah it is universal it's not Universal means a lot of people have this misconception people think Universal means if I'm sitting here I can apply the force on a very far away planet that is not what is meaning of universal Universal means no matter where you go in the universe the law Remains the Same so even if you take the two charges on Mars in other Galaxy still they will apply the same formula but but imagine you drive on the left hand side in India or in somewhere else you drive on the right hand side that is not Universal from place to place it changes so that is the difference between Universal versus non-universal okay very good yes both would exert the same force on each other because of Newton's third law so the force on one because of two and force on two because of one they both are equal and opposite so F12 bar is negative of F21 bar this is Newton's law of motion the third one the third Newton's law of motion action and reaction action and reaction if a body applies a force on other body then this body also experiences the same Force but in the opposite direction that's Newton's third law these two forces and act on two different bodies hence they do not cancel each other obviously imagine this F21 were to act on this one yes they will cancel on that body but no it's not like that this is on this this is on this so they cannot cancel because they are on two different bodies that is your Newton's third law now if you ribu get rid of this p uh uh proportionality what you get is that equality relationship so let's U have a look at it let's have a look at it my dear students so that Force becomes K q1 Q2 divided r² where this K is called as the Kum constant kulum constant which is having a value of which is having a value of 9 into 10 the power 9 in SI units you can very easily get the SI units of it it's not that difficult force is in Newton check this out force is in Newton so Newton is on the top take R square on the top so it will be meter Square charge charge Kum Kum bring it below so it will become Kum Square below so Newton M square perum square will be the SI unit of the kums constant okay as simple as that so let's block this off let's block this off but you will see very often instead of using KQ q1 Q2 by r² that K can be also substituted in some other way yeah uh so kum's law is not applicable in all cases why not it is applicable in which not case you tell me which case you would think it is not applicable you will also see that this kums law is often written down like this 1 by 4 Pi epon not q1 Q2 ided r² this is also fine where that kums constant that K that K is actually 1 / 4 Pi Epsilon 1 / 4 Pi Epsilon that is what you have substituted K as this Epsilon this particular Epsilon KN is called as permitivity it is just a constant guys permitivity permitivity of free space or vacuum permitivity of free space or vacuum will be talking about it in a bit for now just remember 1 by 4 Pi Epsilon is K it is just a constant and this number actually comes from goss's law you might be wondering why is it not 2 pi why is it not just 1 by Epsilon why is it not something else that thought would have come to your head right so the answer for that it is it is coming from gos law which will'll be studying in the another chapter don't worry about it now okay so that is a reason for it so it is the permitivity of free space my dear Warriors and it is 8.85 into 10 ^ minus 12 you can get that from here substitute K as 9 10 ^ 9 move this around and take the inverse you will see it is approximately this value okay everybody fine till this point you can guess the unit of permitivity can you guess the unit of permitivity it will be exactly inverse of the kums constant it will be exactly inverse of the Kum constant so it will be Kum Square by Newton Square M Square sorry not Newton Square Newton M Square Newton M Square it will be exactly inverse because K is on the top Epsilon is below so if Epsilon was on the top K will come below that means it will be exactly the reciprocal of these units yep exactly yep okay uh no no even if the charges are moving kum's law is valid it's that new forces also come into play which are magnetic in nature so that is additional Force but the kums law Still Remains the kum's law Still Remains the electric force is still there apart from the electric force you also get some magnetic force in motional charges that is separate that is additional electric force is still there okay so that is completely additional it is not like your are electric force is changing Electric force is still the same yeah it will probably change with the distance as the distance increases or decreases the magnitude might decrease or increase but additionally a magnetic force comes which you will study probably in the next chapter yep it behaves like a current okay okay all right so um kishori uh let me correct you over there saying that it is not Universal because it is not applicable for spheres or anything that is wrong understand kums law is applicable for two point charges fine but a solid sphere a ring a shell a cube what is it it is made up of point charges so if you add the effect using integration you still get the net force so there is another law which will be coming to it which is called as a superp position in a bit through which you can find the net force acting on a body even though kums law is Val Val for two point charges just like gravitation law is valid for two point masses and you integrate you add up you sum up the effects and find out the net force okay I hope that is clear right yeah yeah y okay so let's let's continue with the next part and that is basically the vector form if I'm not wrong the vector form will also be there yes the vector form of kums law not so useful maybe for board's perspective or just like a very simple objective question it might come but other than that it is not having so much of use so imagine q1 Q2 are the two charges and R is the position Vector on uh R is the position Vector of this charge so let me just show it to you properly R is the position Vector of two with respect to one this is position Vector so position Vector is always going to have a start and the end so this is the position Vector of two with respect to 1 so r21 is basically R2 bar minus R1 bar it is the position position of two with respect to 1 also r21 hat let me show that to you R 21 hat unit Vector is r21 bar divided by R2 1's magnitude which is the distance between them which is nothing but simply put the distance between the two charges this is your unit position Vector unit position Vector unit position Vector so that unit position Vector will be something like this this is R 2 1 Hat then our Force which is there our Force which is there on two because of one that Force on two because of one will have two parts one is the magnitude which is F21 and second is the unit Vector second is basically that unit Vector unit Vector any Vector is magnitude times the unit Vector like any Vector can be 5 IC 7 JC Etc or any magnitude times the unit Vector in that direction so what is the magnitude of F21 force between these two charges it is nothing but K q1 Q2 divided by r21 whole square r21 square but what is the unit Vector that unit Vector is r21 hat that unit Vector which we are talking about is actually r21 hat I hope you can see that this force and this unit Vector are in the same line same direction yep everyone with me on this thank you T thank you so much for all the love so why not substitute put the value of r21 hat over here which we have learned in vectors so it will be r21 bar divided by r21 r21 very good what is r21 into r21 square that's r21 Cube so this will become K q1 Q2 divided by r21 Cube but be careful you also have r21 bar over here so lot of people think sir it became cubic law sir sir now Cube sir is it now inverse Cube law no because even though there is a cube there is R2 one on the top in Vector form so dimensionally dimensionally a meter and a meter will cancel meter square is still at the bottom that's it so that is just the vector form of your kums law as simple as that is this point clear tell this point Samuel you are from eutopia and 12th standard I'm preparing for entrance then my question to you is is the lecture useful for me me or not please tell me honestly Samuel let me tell you a lot of students from Nigeria ethopia I think you are probably one of the first ones but many students from Africa keep watching our classes and I'll tell you I have analyzed our Channel statistics honestly lot of comments lot of students and engagement have or has happened from lot of African countries so if you are preparing for it please go ahead because I have person received some Telegram and Instagram messages direct messages saying thank you sir it has helped me in the entrance exam but yeah I'm not really sure what is your exact syllabus but I'm guessing it is more or less the same that's why many students from Africa are watching it so please go ahead unless and until there is a big mismatch in the syllabus which I doubt is uh going to happen is that okay all right all right shall we continue yes sir it should be the magnitude of r21 Yesa r21 without the bar is the magnitude is the modulus it's the mod value it's the magnitude which is the distance so that's why I did not put the bar yep isn't it chapter one yes it is chapter one yes it's the same thing guys I hope you know I hope you know r21 bars modulus is the same as R2 one without the bar I have told you this in vectors I've told you this in vectors you don't put a bar is that scalar magnitude that's all okay you are not putting the bar so it is the same thing don't get confused over here cool shall we go ahead shall we go ahead yep very good very good CH let's move ahead and here is the first level one question find the vector form of the electric force oh why is it both a and a this is printing mistake I believe so maybe between A and B all right so between A and B find the electric force in Vector form very simple let's try to do this so Vector form the electric force on B due to a on B due to a both are positive both are positive so if I Define a unit Vector over here if I Define a unit Vector over here let's say I call it IAP if I call it as IAP then the force on B will be in the same direction the force on B due to a because both are going to repel each other they are going to repel each other yes it is in the same direction so the vector form of that force will be the magnitude times I times I I defined this as the x-axis this as the Y this as the Zed so it's along x-axis so PC I don't even have to worry about it so much now the force value the force value my dear students my dear Lions what will it be it will be K q1 Q2 by r² it will be k q a QB divided by that distance square and that IAP just follows you don't have to do really much about it okay that's why I tell you that this Vector form is literally not so useful for us because it is just telling me one added unit Vector I mean forget this for a moment if you look at it it is just magnitude into unit Vector so the same thing I've done it's the magnitude into unit vector k value 9 into 10^ 9 q1 value 2 micrum so 2 into 10^ - 6 Q2 value 4 into 10 ^ - 6 distance 4 cm can be written down as 4 into 10^ minus 2 m so hence the denominator hence the denominator will become 4 into 10 ^ - 2 whole squ whole Square over here let's see what do we get now 4 square is 16 4 square is 16 2 4 are 8 8 all right so what are the numbers we are getting 9 into 8 divided 4 square is 16 that's what I'm getting into all the powers of 10 let's see 10- 6 10- 6 will make make it 10 to -2 -12 + 9 will make it 10^ - 3 on the top this will become 10 the power minus 4 over here how can I forget IAP at every stage at every stage okay continuing the process continuing the process this 8 and 16 will cancel two times 9 by two is basically 4.5 this will become 10 the^ minus1 below which is into 10 which is nothing but 45 which is nothing but 45 45 IAP and obviously do not forget the units which is Newton so answer is 45 IAP Newtons is that clear Mala I think you missed that two Mala I think you missed that two yep all right yes yes 45 IAP Newtons so this is how you write in Vector form so tell me one thing my dear students did you understand this is not so useful unless you are writing Bard exams Bard examiners Fascinate this so much they get so happy looking at this formula I don't know for what Joy I mean it's nothing great main thing is this guys main thing is over here over here all right all these are important things other than that it is very straightforward moving on to the next question these kind of questions do repeat in many competitive exams two point charges repel each other with a force of 100 Newton one of the charg is increased by 10% other charge decreased by 10% was the new Force for the same distance all right let's do this was a new Force for the same distance come on my dear students are you going to cover both chapter one and together in one go no BTS Army it is going to be separated like I said today point charges mainly Field Force potential energy dle this is what we are going to cover second part gos law and its applications with geometries and dors that is how the division happens okay so you'll see HCA sir has done a very beautiful division on those chapters I don't like that division in ncrt it is horrible I mean they have mixed capacitors also in it that's like a complete kit that's like the worst arrangement of chapters that you can possibly think of is there in ncrt okay so that's the reason why we follow HC Verma flow all the coaching institutes follow A peculiar flow which is very different from ncrt uh T you are in eight standard and you are able to understand everything wow very good you are going to be one of those students who stick with me till 12th and then tell me sir you know I am there from enus times I received few comments few days back sir I know you from V enus day I'm like oh my God how do you know enthus that's channel name when we started it was called enthus then it became enlight now it is just called vantu J English so and they were like sir I was studying from you from 8th standard and now this time when you are discussing the J Mains paper you know I did it very well and now I'm getting a good college so I'm guessing that will be the same case with you after couple of years maybe around four five years down the line right congratulations if you are understanding everything definitely it's very useful for you please go ahead watch it right okay so my dear students what is going to happen over here two point charges repel with 100 Newton right okay so one charge here one charge here I don't care what the values are I'll just put QQ how does it matter okay and what happens is the force of repulsion or attraction is 100 100 okay now what happens the next time you increase the charge by 10% tell me one thing if you increase any quantity by 10% it will become 1.1 times imagine you have 100 rupees I increase 10% it will become 110 110 is 1.1 times of 100 110 is 1.1 times of 100 so if this is Q 1.1 times of Q is basically the new charge is basically the new charge so can I say this is 1.1 Q same way think about it if I reduce the other charge by 10% how much will that be if it is 100 it becomes 90 it is9 times 100 so it is0 n times the older charge so should I not say it is n times of capital Q there will be a new force between them there will be a new force between them yes or no so this this force will be K q1 which is 1.1 Q into .9 Q divided by R squ best part q q and K and R assemble just like Avengers Assemble the charges K and R assemble what you have over here is 1.1 into .9 1.1 into .9 interesting thing to note is K QQ by R square K QQ by r² is actually 100 Newton that's the original Force so my dear students that's nothing but 100 and what you have over here is 11 * 9 which is 99 which is 99 because of the decimals hence it will become 99 Newton 99 Newton is the answer very good sha very good mesu excellente is there any more session for bitat as of now sham nothing planned because we have lot of sessions on the channel older sessions also you can watch it okay that is something which you can use very good understood o Clearo shall we go ahead to the next question wow what a question we have two free charges q and 4 q are placed at a distance of D apart a third charge is placed in between of them at a distance of x from Q such that the system only is in equilibrium then what do you think that charge and that distances is the next level question let's try to visualize this first what is exactly happening three charges q and 4 q are placed okay Q let me put 4 q this is Q This is 4 q and distance is D distance is basically B the distance D apart so so obviously this q and 4 q will repel each other they will repel each other let's say I call it as F1 the force of repulsion between them is F1 okay just keep it aside now Third charge is placed at a distance of x from small q okay so let's say at a distance of X you place another charge which is capital Q This distance is X now think about it think about it my dear students if the system has to stay in equilibrium this is only possible if you take any charge and the net force is zero so for example s let's take this small q charge the small q is experiencing repulsion because of 4 q left side so to stay in equilibrium for it to stay at rest it must experience opposite Force by something else who is that something else the capital Q charge so hence there must be an attraction between them because of that capital Q let's say I call it F2 these two forces should balance each other yes or no these two forces should balance each other all right everyone everyone okay very good awesome now if you notice all the answers are negative all the answers are negative because 100% it has to be because only when they attract will this Q charge remain at equilibrium so let's equate the two F1 will be equal to will be equal to FS2 what is the value of fub1 between this and this between this and this how much will it be it will be k q 4 q k Q4 Q divided by d square is equal to what is FS2 think about it the force between these two it it will be nothing but k then Q then capital Q divided by what um just x² just x² so you can see one of the q k has got cancelled and what am I left with over here is just this four this number Q This d s is there and on this side what is left is uh capital Q and basically x² but this is only one equation I have two unknowns one is the capital Q value second one is this x value I want to find that X also so let's do one more thing over here let's do one more thing over here this and this this and this will also exert some force between them they will also exert some force between them so this capital Q on this 4 q will apply an attractive Force let's say F3 so for this to stay in equilibrium these two should be equal these two should be equal so guys can I not say F3 will be equal to fub1 F3 will again be equal to basically fub1 right so what is the value of F3 think about it F3 will be k 4 q k 4 q into capital Q divided by this distance will be D- X this is D this is X D- X so that's why this will be d - x² is equal to is equal to fub1 the same F1 which we have used over here so it will be repulsion between these two charges which is four uh sorry which is basically k q into 4 q / D ² now when you cancel when you cancel K when you cancel Q what you are left with is 4 q ided D sare and on the left hand side you are left with 4 capital Q / D minus X whole squar you have this equation you have this equation what will you do you have these two equations what will you do my dear Warriors I think you can see it right over here you can equate this with this you can equate this with this to find the answer everybody seeing that 4 q by d s 4 q by D sare equate this with this Q by x² 4 q by D- x s if you want I will do it on the next page I'll do it on the next page so 4 4 q by d - x² will be equal to will be equal to this one Q by x² will be equal to Q by x² q q will get cancelled you will take 4 with x² on one side and d - x s on the other side taking Roots it will become 2x isal to D - x so therefore 3x therefore 3x is equal to D therefore X is equal to d by3 x is equal to D by3 can you see D by3 in both the options it is there so B and D options get eliminated everyone yes but R for fub1 is D minus X whole Square for F1 what is force F1 it is between q and 4 q the distance between q and 4 q is D so that is why I have used D F1 is the force between these two and the total distance was D that is why D has been used clear now what will you do what will you do next what will you do next yes think about it yeah once you have got the value of x substitute it either here or here you will get the next answer let's say for example here let's say for example here only you can substitute and see what is it that you get so it will just become 4 q by d s will become will become Q by x² X I got it as X I got it as d by3 x I got it as D by3 so D by3 whole Square D Square D Square will cancel 9 will go on the top so 9 Q by that's it 9 Q by d s if you want I will write it on the next step and 4 q by d s d s d sare will cancel therefore from this what will you get is the value of capital Q you want the value of capital Q so capital Q D square has gone it will be 4 by 9 * of small q this is all magnitude wise this is all magnitude wise but sine wise I know Q should be negative because it is going to attract so 4 by9 is there as option number a and that is the correct answer that is the correct answer understood how to solve this understood how to solve this okay account I had made a video on bitsat uh strategy just check out that video or use any bitsat test series uh video in that you will find the test series uh link attached with the coupon code okay for $4.99 rupees any video or if if you are not able to find it leave a comment after this video our team will reply to that comment with that particular test series uh you know which you can buy all right next question 10 micrum charge is divided into two parts and place 1 cm apart so that the repulsive force is maximum how should the charges be how should the charges be any short method k no this is the method and the reason why I take long time is because I want to explain everything but when you do it in your rough sheet trust me you will do it within one and a half minute not more than one and a half minute with good practice okay initially it looks long with practice one and a half minute Max to Max 2 minutes max to Max tuck you would have solved so many problems okay these two charges will attract and repel okay forces are equal tuck tuck tuck you will not even write this you already would have calculated that K and K will cancel and all of that immediately these two charges will repel and attract okay again equation for this okay rhs are equal okay let me equate this with this Tu tuck tuck you will solve two options eliminated substitute X over here tuck tuck tuck solve it you'll get the answer it is not that difficult okay so with practice you will find it to be easy initial days it's always like that just like when you found vectors very tough you understood I cap J cap K cap probably after quite some time just remember that time how much time you took for understanding chematic equations or unit and all of that right so it always takes some time okay yeah Motion in 1D next week B yeah okay so what about this whenever you have force between two charges value is K q1 Q2 by basically R square I can't touch R I can't touch K but I can touch q1 and Q2 but there is one thing about q1 and Q2 the sum of the charges q1 + Q2 is going to be 10 I want to split the charge somehow so that the force is maximum now I'll tell you just just hypothetically take some values like this is 1 this is N9 this is 2 this is 8 this is three this is 7 this is four this is six this is five this is five after this it's just a repetion because this will become six this will become four and so on and so forth if I just take the multiplication of these two because I want to make the force maximum so their product should be maximum but their sum is constant 1 into 9 9 2 into 8 16 7 3 is are 21 6 4 are 24 5 5 are 25 24 and so on and so forth do you notice one interesting thing that it is maximum over here this is the maximum value and this is exactly what we want to do we want to make the force maximum that means the product should be q1 Q2 should be maximum hence both the charges should be equal so the answer should be B correct in fact let me tell you one very interesting property which you can also keep it in your notes if the sum of two numbers is constant is constant example X1 + X2 is equal to C then their product then their product then their product basically X1 * of X2 is maximum is maximum when they are equal is maximum when they are basically equal very very interesting thing basically X1 should be equal to X2 which should be equal to constant by two if X1 equals to X2 then both of them should be half and half of their sum then their product becomes maximum you can see that right over here is that clear yes very very easy and uh this has been asked in J meanss okay moving on to the next principle which is the principle of superp position and this is the reality of your life also this is the reality of your life also so my dear students just imagine you know there is a pandu there is a pandu sincere pandu what happens is his mom tells his mom tells this pandu go bring bring potatoes bring potatoes from the market his dad tells listen pandu you go get you know something go get some paint from the shop go get some paint from the shop the teacher tells the teacher tells go study get some marks go study get some marks a friend tells a friend tells listen come with me for the party come with me for the party what will this pandu do what will this pandu do well don't think of yourself and tell me the answer because I know what you will be like sir very simple is this even a question why will I go to the market and buy potatoes why will I go to the market and buy paint why will I go and score marks my friend is calling me for party I'm obviously going for the party sir okay that is you but Pand you know what he's going to do he's going to do everything okay V have any faculties from Kerala oh many faculties you come to the office so many Malo are there most of our video team is from Kerala some of our faculties are also from Kerala in fact on my vant English Channel gopa ma is a Malu yes gopa ma'am who teaches awesome biology she is a Malu okay so this pandu will end up doing everything this pandu will end up doing everything and that's why his pandu guys he's an allrounder so he's listening to everything same thing even a charged us imagine imagine like for example this charge over here you are placing it near other charges this charge will repel this charge will repel this charge will attract so what will this charge do it will experience a net force it will listen to all these charges and the vector sum of the forces will apply on this particular charge so basically this is called superpositioning all that all the instructions given by all these people Mom Dad teacher friend blah blah blah they are being superimposed they are being super imposed on pandu and pandu ends up doing everything same way this charge also experiences the net force given by the vector addition this is what you can see over here this is the principle of superpositioning as simple as that is that clear everyone SAA quite late we are r p diar why Pam because you're going to go to the party or no okay cool let's go let's go use the super positioning principle in some of the problems wow directly level two question so I hope you will be able to do it what say okay ready for the challenge let's do this okay directly level two guys charges Q minus 2 and minus Q are on the sorry are held fixed at the three corners a b c of an equilateral triangle of side a find the electric force on the charge at C due to the rest of the two interesting let's try to solve this let's try to solve this by first of all taking up a triangle let's draw a beautiful triangle over here okay beautiful triangle let's mark the vertices and the charges let's mark the charges and the vertices vertex a this is vertex B this is vertex C on vertex a the charge is basically Q charge is basically Q on vertex B it is basically minus 2 q and on C it is basically minus Q okay perfect question is find the force on charge C okay this P Charge c will experience Force because of this as well as this what is this Q trying to say to this Q what is it trying to say to each other come on think about it this q and this minus Q they are getting attracted why because they are opposite in nature so let's say I call it as F1 no harm right what is the value of FS1 it will be magnitude wise magnitude wise k q q divided by side well the side length is basically a the side length is basically a so K QQ / a square which is k q ² / a square that is the force of attraction between the charges kept at A and C because they are opposite in nature what will B and C say to each other both are negative both are negative right so what will happen sh well if you're in class 11th it is not mandatory for you to see it but yeah if you are done with your syllabus most of it whatever has been taught till now then yes please go ahead with it you will definitely be learning whatever you anyways you have to learn after one year so you'll get more time later on so that's a very good move if you want to do it so they are going to repel each other again and the repulsion will be along this line and that force will be FS2 which will be K QQ magnitude wise k q and 2 q q 2 Q again divided by a square so it will be 2 k q s divided a square oh these two forces one force is like this fub1 the other force is like this over here this is F2 can you guess the angle between these two forces come on my dear students it's not that difficult because this internal angle is 60° of an equilateral triangle so naturally that angle should be 120° so just mark this angle as 120° and what I want to do now is find the net force I want to find the net force so this is the net force and what is the net force use the vector addition formula so fnet fnet will be root of root of fub1 s + FS2 s + 2 fub1 F2 cos 120 that is what the formula is all right but you know what the best part is in F1 and FS2 fub1 and FS2 k k q Square Q square a square a square three things are common so I will take k Q ^ sare by a square common okay and only inside the root what else will remain just think about it in fub1 k q sare by a square is taken out so don't worry only one is remaining so 1 square plus in FS2 only that number two is remaining so 2 s + 2 into 1 into 2 into cos 120 is half is that right COS of 120° is half wow very good so what will happen now just check this out 2 two cancels this will become min-2 this will become min-2 2 sare is 4 4 + 1 is 5 5 - 2 is 3 so I'll have root3 over here so k q ² < tk3 and you will have a square over here that is the answer that is the answer for your net force acting on that charge Q minus Q at C is that absolutely clear my dear Warriors how that root of three came yep don't we have to take the sign kishori we have already considered the sign by showing the direction think about it how did I realize that F2 is this way because I know that both are negative so if something has been considered don't consider it again while solving physics problems just like when you show that velocity is like this and you show velocity is like this then don't write velocity is negative or you know if if I put minus V bar if I put minus V bar then it means whatever I've shown is wrong it is actually on the right hand side so that's how it works so same way my dear students can you see q and minus Q will attract I've already shown their attraction so already the angles are marked with the correct signs taken into account and only the magnitudes are shown so it's just like a simple vector addition problem once I know these are two forces individually I have to find the resultant Force that's all is that okay everyone Clearo shall we go ahead shall we go ahead to the next okay now kum's law in a medium which is other than vacuum this is very very again crucial it will be useful in the next part uh as well okay and I hope as you watching this you're smashing the like button and subscribing to the vantu J English Channel Channel my dear students okay make sure you are subscribing make sure you are liking this video the reason why I ask you to like is obviously it is like a small Guru for us but also at the same time YouTube understands that you are interested in J physics so it will recommend you more content like that and you know it will be helpful for you only yeah if you have Vector backlog cover it right now how Shri I just made a video right on vectors where did it go J English Channel I hope you had seen this where is it vectors very simple class 4 hour class is there within four hours you can complete vectors if you watch this that's it and after that you have to solve problems okay so watch the vectors class I have also [Music] done I've have also done units and dimensions it's done okay it's done okay so two chapters of 11th are done now we are on to where is it now we are on to electrostatics uh Tuesday I'll be doing gos law so this unit of electrostatics and gosla is over and next week again uh second class will be onedimensional motion 1D motion okay that's what we are going to focus on H okay so where is it let's go yeah kum's law coolum's law in a medium other than vacuum okay yes definitely you can complete it soon now see I told you when you have a medium apart from sorry when you have no medium that is vacuum then the electrical force of attraction or repulsion is given by 1 by 4 Pi Epsilon q1 Q2 divid r² this is basically in free space nothing is there it's completely free but the moment there is some kind of a medium then what happens the force changes it will become 1 by 4 Pi Epsilon of the medium into q1 Q2 ided r² this is the force inside inside the medium inside the medium this Epsilon m is no longer the permitivity of vacuum instead this is called permitivity of the medium permitivity of the medium which is a medium specific property like you have density refractive index coefficient of friction Etc these are medium properties material properties so any medium has a property called as the permitivity of that Medium which has to be EXP experimentally determined okay it has to be determined by conducting some experiment only then you can find it out and there are tables through which you can get it in the exam you are directly given this value or you are asked to find out by some other information this Epsilon m is actually is actually something called as K into Epsilon KN Epsilon not is permitivity of free space this is permitivity of vacuum lot of people will think this G is the Kum constant no be careful this symbol is the same but the meaning is completely different this K is called as the D Electric constant of the medium dielectric constant dialectric constant of the medium dialectric constant of that particular medium very very important so if I substitute it on the next slide and show it to you do I have a slide yes okay so I'll substitute it and show it to you that new force will become that new force will become 1 by 1 by 4 Pi instead of Epsilon M I will write it as K * of Epsilon KN K * of K * of Epsilon KN and then the remaining things as it is q1 Q2 / r² but 1 by 4 pi epon q1 Q2 by r² is exactly this force is exactly that old Force if you notice is exactly that old Force so why not write it as that old Force as it is this is our new force and what is it divided by it is divided by K so this is also a very very important relationship the new Force reduces K times the new Force reduces K times exactly than the older Force K is the D Electric constant of the medium okay and this is also very very important my dear students this is also very very important the permitivity of the medium is permitivity in free space into the dialectric constant okay so wherever you wrote Epsilon KN it will become Epsilon M basically of the medium in in general the force becomes K * less as simple as that as simple as that very good okay perfect I put the theory slides also for all of you just in case if you want to watch it let's say if I put a question like this example okay this is level one okay example if if the force or rather find the force between between 2 kums and 3 kums kept at 3 m away in a medium of of dielectric constant of four question mark also what is the permitivity also what is the permitivity of the medium that is also the question come on my dear students try and solve this try and solve this quickly okay okay so very very simple all you have to do is simple substitution in the formulas oops yep let's do this the new force will be because it's in a medium instead of instead of 1 by 4 Pi Epsilon it will be you know that constant which will be divided by the dialectric constant so it is basically 1 by K * of 1x 4 pi Epsilon q1 Q2 / r² this K is not kums constant this is dialectric constant which is four this value is 9 into 10^ 9 q1 is 2 kums Q2 is 3 kums distance 3 m so 3 Square 3 square and 9 cancels 2 and four also cancels it will become 1X 2 so I think it will become 3x2 so 3x 2 into 10 the^ 9 newtons that is the answer that is the force between them just check this out if this is clear then we'll go to the next part yeah 3x2 yeah basically 1.5 10 ^ 9 excellente similarly what about the permitivity of that Medium it will be K * of Epsilon K is 4 Epsilon KN is 8.85 into 10 the power -12 come on multiply this four times 8 4 are 32 85 into 4 come on do this how much are you getting how much are you getting yes come on my dear students how much are you getting 85 is less than 100 by 15 15 4 are 60 so6 less so it should be 35.4 so 35.4 into 10 ^ -2 just check this out that is the permitivity of the medium as simple as that that yeah rotational motion will take a lot of time yeah it will come after quite some time not this month for sure because we have to go to 1D then 2D then Newton's laws and friction then work energy uh circular motion a center of mass collisions rotation okay very very late it's probably going to come in the month of July end or probably August okay it's going to take some time we are going to try and complete the syllabus as much as possible by August or September that's our Target it might go here and there obviously you always need to set a Target only then we'll start to achieve things so that is our Target guys okay clear let's move now to the next part which is electrical field intensity I hope till now whatever I have taught is very nicely embedded in your head it's stuck in your head and you're learning properly okay let's go to the next part which is field field means any charge around it you know it will apply forces on other bodies other charges using that field it's like your Wi-Fi signal like you know I have my phone I have my phone it is able to connect to some router or is able to communicate to other phone how through some electromagnetic waves so this phone up applies some effect on some other phone or other telecommunication device so the charges also wirelessly they communicate to each other why this field please understand this field is not electromagnetic it is not gravitational it is something else only it's just an hypothetical concept but it is there but it is there yes yes one it's going to be Beyond April 25 till me don't this channel is going to continue yeah don't worry about it just like I hope you saw what and all we did for your seniors in fact next year it will be even more understand that because this year you know I was just concentrating mainly on the content and making sure that you have all the kinds of lectures for all these subjects as much as possible this year it's going to go beyond the content it is going to go to more of awareness it's going to go towards colleges branches and so much more okay once we have the content ready on the channel okay already we have a lot of content on the channel but I want to take the content to a Next Level okay that's the reason for it so electrical field intensity is defined as electrical field intensity is defined as the electric force electric force per unit test positive charge this is what electrical field intensity is defined as so just imagine that you have some body okay this is some charged body this is some charged body and let's say I want to find the field at this point to find the field to find the field at this particular Point what will I do I will bring in a test charge I will bring in a test charge and let's say the test charge is + one Kum + one Kum and on that test charge I will find out I will find out how much force has been applied how much force has been applied it could be this way this way depends on what these charges are it could be even this way it could be even this way depends on what the system is for example I'm just showing it to you over here the forces is example you know uh 30 Newton example it is 30 Newton then I will say wait a minute oh electric field is force per unit positive charge so the field on it the electric field by the way the symbol for that is e that electric field is nothing but the force which is there which is 30 Newton divided by divided by the unit test positive charge which is + 1um hence the electric field electric field magnitude wise is 30 Newtons per Kum 30 Newtons per Kum as simple as that okay so this is the magnitude of it this is the magnitude of it it is 30 Newtons per Kum everybody till this point till this point capacitance my old videos might be available yeah so the way we by which we Define electric field is nothing but the force force per unit test positive charge whatever charge I have placed over here electric field is force per unit charge and you can see the uh unit of electric field is Newton per Kum later on you will also see it is also volt per meter we'll come to this unit later on okay as simple as that also note one important thing it is a vector quantity it is vector quantity in the direction of the force on the positive test charge positive test charge why positive it is just a convention because somebody will say negative somebody will say positive we have to stick to something that's why we stuck positive that's all nothing great about it okay so this is the very very important formula this is how we Define electric field you can also go one step ahead one second yes you can also go one step ahead and say let's say for example at some point at some point let's say the electric field is e and you happen to place you happen to place a charge over there you happen to place a charge over there then the Force which acts on it the force which acts on it will be nothing but the charge times the field will be charge times the field very very important it is the same thing as the previous formula if you notice if you shift that Q over here Q into e is F Q into e is basically F that is exactly what you are getting you can also see that the electric force that the electric force force and the electric field are in the same direction if Q is positive if Q is negative then the force will be opposite so electric force is parallel to the electric field is parallel to the electric field if the charge is positive makes sense because if this is a positive charge versus you take a negative charge if the field is here if the field is here you will see the four force will also be in the same direction but the electric force the electric force is anti- parallel is anti- parallel to the field is anti parallel to the field if the charge is going to be negative because you're multiplying it with a negative number you multiplying it with a negative number negative times a vector will change the direction of the vector positive times the vector will just stretch the vector in the same direction negative times will make it Opposite positive times will keep it in the same direction that is what it is is this absolutely clear my dear students these two points why the direction may change or may not change this is the example of a proton this is the example of an electron yep thank you Daka excellent okay okay now that we have understood it till this point uh we have done this okay now let's go to the electric field due to a point charge that is very very important formula electric field intensity on a point charge on a point charge sorry not on due to due to a point charge my bad due to a point charge so imagine I I have a charge capital Q and at some distance R I want to find what the field is going to look like so I want to find the field at this point so I will quickly introduce at this particular point a small test charge which is small q so immediately I will say electric field is the force acting on that point force acting on that point upon that charge which is there so the next step will be nothing but okay I'll just put 1 by Q as it is the electric force value will be K between these two k q q divided by r² notice how this q and this Q will get cancelled this q and this Q will get cancelled and I am just left with I am just left with K capital Q ided r² that is your electric field due to a point charge k q / r² is this absolutely clear my dear students is this absolutely clear my dear students also notice one important thing over here is as you go far away the field reduces as you go far away the electric field will definitely reduce and you can plot it on the graph so if you plot this field versus distance graph it will be a curved line because electric field is inversely proportional to the square of the distance as you go far the field rapidly reduces es reduces and reduces clear very good so we can see the same thing over here also electric field due to a point charge now interesting thing to note is if you are near a positive charge the electric field on any other positive charge around it will be radially outwards does that make sense because think about it if I put a neg if I put a test charge over here the electric force will be like this if I put a test charge here due to this it will be repulsive due to this it will be repulsive due to this it will be basically repulsive but here if I put that positive test charge it will be attractive here if I put it it will be attractive here if I put it it will be attractive here if I put it it will be attractive here if I put it it will be attractive so it is attractive around a negative charge it is repulsive around the positive charge so these are the test charges that we place to check the direction of the electric field very good so let's move ahead and also let me tell you one important thing that electric field also follows super position so electric field also follows super position principle there is uh no doubt about it meaning if I have uh you know let's say a charge over here let's say I have a charge over here on on that charge there are many fields let's say field one is like this due to some other thing it is like this due to some other thing it is like this and so on and so forth and there are many such Fields n so the net electric field so the net electric field is the vector sum of all the fields so it will be E1 bar plus E2 bar plus n Bar okay okay so you have to take the vector addition of all of them to find the net electric field as simple as that okay so let's solve some questions coming up on your screen and here it is two charges are there 20 cm apart the field VI to them will be zero where draw the diagram first without that you will not get anything draw the diagram first only then you will get anything okay har and dwaram please talk in English other students will not understand plus English Channel for you or else then we would have kept quiet with Hindi Channel no all these years you struggled because you did not have English channels you have English Channel use it talk in English okay come on so we have two charges one is basically four micro the distance is 20 cm from 9 micrum okay somewhere the electric field will be zero one thing I know the positive charges always give the fields radially outwards so this will try to apply field like this this will try to apply the field like this if you notice here somewhere these two Fields will cancel but if you go here these two Fields will add if you continue here again these two Fields will add so they are not going to cancel here they cannot cancel here because four and nine both give fields in the same direction in this region only in this region this four will give the field like this this nine will give the field like this there is a good chance they will cancel somewhere in between so I don't know where they are going to cancel let's just ass assume that point and that distance is X basically so due to this the field will be here due to this nine the field will be here so field due to four field due to 9 this is how the directions are obviously the field due to 9 and the field due to four should cancel because the net field is zero at this point here you will see that the net field is zero because these two fields are canceling out each other due to 9 my micrum what should be the field by the way you know this distance you know this distance this is basically 20 - x this is basically 20 - x okay so check this out field due to a point charge I just give you the formula KQ by r² come on SO field due to 9 will be k q q is 9 micro divided r r is basically 20 - x cm square that is what it is electric field due to the 4 micrum charge it will be k q is 4 micro divided by distance is basically X cm and square you might be wondering sir why do you not convert centimeters into meters second point you might be asking sir why did you not write 4 micrum or 9 micrum as 4 into 10^ minus 6 what is the reason behind it what is the reason behind right think about it yes think about it my dear students because I know they are going to get cancelled same units on LHS and rhes will anyways get cancelled so this micro over here this micro over here this centimeter here this centimeter here anyways get cancelled so don't bother converting it exactly gishi so continuing the journey what will I get even K got canceled by the way uh 9 o 9 by 20 - x whole squ is 4 by x² taking roots on both sides 3x 20 - x is = 2 by X cross multiply 3x is = to 3x = 40 - 2x uh take 2x on this side so it will become 5x is equal to 40 so X will be 40 by 5 which is is basically eight always in centimet everything was in centim so answer is 8 cm from the first charge which is option A which is option A done and dust it very good excellent yes ashant current electricity it will take some time Z not so easily okay it's going to take some time yeah next week gos law after that week so next week is gos law after that week will be current electricity then we will go to Magnetic effects sources and all of that every week parallely we will be running the show okay moving on to the next one this question which was asked in J Mains 24 tell me will you be able to solve it the same thing same thing has been applied I just wanted to show you how same type of questions have come in J Mains also charges q and 3Q are separated at distance R the resultant field is zero the value of x is same type so so this should be done as homework I want all of you to post the answers in the comment section okay all of you are going to post the answers in the comment section now let's go to the next few geometries which are again based on the superp position principle which do not include Goss law see shell sphere sheet line charge all these geometries I will do in the next lecture because they will be very easy to be done when you learn goss's law so whatever geometries we are learning here are ring and points because they do not need goslow so let's take a Charged ring and find the electric field formula because of a Charged ring okay because of a Charged ring guys so field due to a charged ring very interesting let's say for example I take a ring like this see if you able to visualize this ring in three dimensions see if you able to visualize this ring in three dimensions okay this is your probably x-axis this is probably your x-axis this is probably your Y axis this is probably your Zed axis x y and z are you able to visual is this R yep now um yes yes s Surya I'll be completing uh kinematics kinematics one day is there next week yeah that's what is going to happen now in this charge ring okay if I take the central point just visualize what will happen to the field if you are exactly at the center this is a charged ring each charge on the ring with will give an electric field like this you take any charge it will give an electric field like this you take any charge it will give an electric field like this you take any charge it will give an electric field like this you take any charge it will give an electric field like this take any charge it will give an electric field like this now all these fields are symmetrically distributed all these fields are distributed in the same plane and they will get canceled out agree or disagree so what will happen to the net field at this point it will be zero so one thing I think you should agree upon is the electric field at the center is zero because they get cancelled out because of the diametrically opposite charges diametrically opposite charges the fields will get cancelled out one thing is very very clear but the problem happens if you're not at the center but at this point now say for example you take a point over here you take a point over here okay let's say [Music] oops let's say you take a point over here okay at this particular Point obviously the field will not be zero because there is some component which will be pending component which is unbalanced over here and how to visualize that I'll tell you what you do do one thing draw a line from any charge to that point draw a line from any point on the charged ring to that point any point on that charge ring to that point any point on that charge ring to that point any point on that charge ring to that point just visualize this is this not becoming like a cone if I draw all these blue lines dotted lines is it not becoming like a cone my dear students is it not becoming like a cone the curves are surface area yes or no very good very good excellente so my dear students each of these charges along this line will apply an electric field of their own so if I consider if I consider a small DQ charge over here a small DQ charge over here okay D capital Q due to that DQ there will be a small electric field like this in this particular direction there will be a small electric field like this in this particular direction okay and I will call it as d e and every charge will give the D D D D D like that in different different directions like this as if they are on the curved surface of a cone as if they they are on the curved surface of a cone these dotted lines make their own own cone and the forces they make another cone in themselves they make another cone in themselves just visualize this these are the forces these are the force sorry Fields the fields themselves make another cone in themselves the resultant of all of them the resultant of all of them 100% should be in this direction should be in this direction because each of the D will have two components one will be in this Direction one will be in this direction which I call it as de in the X Direction and the other one will be the electric field in the y direction electric field in the y direction these y components these y components will cancel think about it one y will be here one y will be here one y will be here the other y will be here other y will be her other y will be her they will all end up cancelling out each other they will all end up canceling all each other but it is this DX whose integration will give you the net field when you add these DX X components of all these small small Fields you will get the net electric field are you able to visualize this give me a thumbs up then we will go ahead give me a thumbs up we will go ahead till this point is it clear so what is the value of this D well it is K okay I need this distance also if this is X and the radius is R then how much is this distance going to be it is going to be root of r² + x² so it will be K into DQ divided root of r² + x² r² + x² s r² + x² root whole square that root will anyways cancel out I need the X component of it to find the field so the net field is integral just now I told you it is nothing but integral of d e x which is that electric fields which is basically which is basically this particular electric Fields component which component will it be this component if I take this as Theta if I take this as Theta it will be nothing but D cos Theta it will be nothing but D cos Theta so let's integrate and see what do we get guys so integral what is the value of d d value I just put it over here it was K DQ ided r² + x² root has gone what do you think cos Theta is well if You observe carefully you will realize if you'll observe carefully you will realize this is the radius uh this this is basically your hypotenuse the bottom is basically X if this is Theta obviously even this is Theta obviously when this is Theta this is Theta even this angle is Theta everywhere so what is cos Theta what is COS of theta adjacent by hypotenuse hypotenuse is root of r² + x² so therefore it will be nothing but X ided by root of r² + x² now the best part k x r everything is constant lot of you think I have to integrate this complex thing but actually no you will see K is a constant X is a constant see for all these charges X is the same even Theta Was the Same by the way these two when you multiply you will get r² + x² raed to 3x 2 what is remaining inside is just the integral of DQ is just the integral of DQ meaning you add all the charges on the ring you add all the charges on the ring that's it you will get the total charge hence the net electric field hence the net electric field will be k q x / r² + x² whole ra to 3 by 2 that is the answer which is what we had put over here k QX / r² + x² to 3x2 is that clear everyone yep cool awesome awesome awesome is derivation important yes these derivations which are do here are very important okay from meain as well as board's point of view uh more than means I say Advance Advan and Boards point of view it is important but last year in boards they did not ask d equations so it is surprising so every year you know they have different surprises obviously you don't want to keep it till the end okay so that was the electric field due to a uniformly Charged ring and the best part like I said before at the center the electric field is zero at the center at x equals to 0 electric field is zero and also you will see as X becomes very large then electric field tends towards zero when you go real really far away makes sense right I mean think about it why should that happen because as you go really really far away you are very far away from The Ring The Ring will have negligible effects so the field becomes zero so that is why the graph of that field first starts from zero climbs up and again comes close to zero so it becomes maximum at this distance which is R byun2 remember this value this comes bya Maxima Minima concept it becomes Maxim Ma imum at R byun2 yes is that clear okay very good the next important uh formula that you should know is this one no need of derivation for this but anyways if you want to know the derivation it is again the same thing you take DQ charge and then because of that you find the field that field will have two components the X component will cancel the Y component here will add okay and then you add them by integration with suitable limits you get this as the answer so the electric field due to an arc not a complete ring but an arc at the center is given by 2 K Lambda by R sin Theta by 2 Theta is the complete angle you might be wondering what Lambda is Lambda is linear charge density linear charge density it is basically how much charge is there per unit length the unit of Lambda is Kum per meter Kum per meter how much charge is there per unit length you take one meter in that how many are there that is linear charge density Lambda so 2K K is kums constant Lambda by R into sin of theta by 2 as simple as that as simple as that okay nothing great about that formula so let's say for example let's say for example you are given a semicircular ring which is charged like this a semicircular ring which is basically charged like this and you want to find the field because of that the field will be in this direction that field by this Formula 2 K Lambda ided R sin Theta by 2 check what Theta is over here the Theta will be 180° or basically Pi so let's say it is also given to you the charge on it is q and the radius of this is basically R so what is Lambda going to be just think about that as well so Theta is basically Pi radians what is Lambda charge cube is distributed on this ring so charge Q is distributed on the semicircular ring the length of that wire is basically just pi r not 2 pi r just P pi r because it is a semicircle so Lambda also I know so just substitute it and you will get the answer so it will be 2 * K is basically 1X 4 Pi Epsilon okay or you can just leave it as K also no harm just see how the options are divided by R Lambda is Q / < R and S of s of < by 2 sin 90 is 1 so this will become 2 k q / < r² that is is the answer 2kq / PK r² is that okay everyone with me yes that is the correct answer just direct questions do come on these kind of things right sometimes you might have a simple this kind of question also has been repeated many times simple question I'll just show it to you there was a ring given and the question is at a distance of the radius only this is Q This is R what is the electric field at that point what is the electric field at that point so again you have to use the Formula K QX divided by r² + x² to 3x 2 so k q X is nothing but R okay just substitute r² + r² whole ra to 3x2 so it will be K QR / r² to 3x2 will become R Cub just take that R out side all right so if you see it will become r² whole to 3x 2 what is there inside is 1 + 1 whole ra to 3x2 I just Tak an r s outside so this will become R CU so it will become K QR divided R Cub this is 1 + 1 2 2 Cube 2 cube is basically 8 8 ra to half so it will become k q r r will cancel it will become r² root of 8 is basically 2 < tk2 is basically 2 < tk2 so the answer is KQ by R S 2 < tk2 that's it okay clear everyone okay awesome awesome right perfect so these kind of questions again standard let's complete electric field lines and and then we will have a break we'll complete electric field lines quickly and then we are going to have a break okay these questions are also very straightforward we'll complete electric field lines before going to the break chandria this is more than neat so this is definitely enough for NE in fact it is more than need because we are going to J level okay understand that now see we learned about electric field electric field is the force per unit charge but when I write it down sorry when I draw it down graphically those things are called as electric field lines it's a diagrammatical experience of how the field travels how the field applies in which direction so when you draw it that is called as the electric field lines and these electric field lines give a sense of what might happen if you place a charge what direction will it move where is the effect going to be strong where is it going to cancel out where is it going to be attractive so that idea you get using the electrical field diagram and these lines which you draw are called as the electrical field lines so how do those electric field lines look like let's see first of all imagine you take a positive charge okay and you want to see how the electric field lines look like so what you do is you take a test charge you take a test charge over there and you're like okay on the test charge the electric force is like this hence the field will be also in that direction you move in that direction and place the charge here check where is the force force is in this direction but it is not as much as before it is slightly less but the field will also be in the same direction so you continue in the same direction reach here Force again like this field same direction so field is here again move in the same direction reach this point and you continue doing this continue doing this as long as it takes okay and that is your electric field line if you do the same thing over here the electric force will be here field will be here you move by the same amount in the same distance sorry in the same direction again find the force and the field in the same direction move by small amount see what is the force and the field in the same direction continue your journey and you will see this is another electric field line so these are called as electric these are called as electric field lines these are called as basically electrical field lines it so happens that for a positive charge for a positive charge these electric field lines look something like this radially outwards for negative charge they are radially inwards positive radially outwards for negative radially inwards that is what also I have shown over here also positive radially outwards Negative radially they will be attractive towards each other if you take just two positive charges just two positive charges you will see that their net electric field lines look something like this as if they don't love each other they hate each other they will bend they will basically Bend away from each other and it will look something like this it will look something like this my dear students this is how it looks for two positive charges whereas if you take two negative charges whereas if you take two negative charges and maybe one of them is more negative than the other one of them is more negative than the other then one of them will dominate the other one of them will dominate the other there will be more field lines from the more negative charge so prob hope you're going to see something like this one field line here one field line here very few field lines will come from this okay and um maybe from here it will be like this probably this is what you might see this is what you might see something like this okay very very interesting diagram one is more negative so more field lines on it one is less negative so less number of field lines on it so this is how the diagram basically might even look like okay so we'll have more field lines coming onto this negative charge versus this negative charge this is how it looks like for two positive versus two negative charges similarly if you take one positive and one negative charge it will look something like this one positive and let's say one negative charge okay so you will see that the electric field lines will look something like this they will go from the positive end at the negative go from the positive end at the negative go from the positive end at the negative charge this is how the electric field lines look like okay this is how the electric field Lin lines look like they'll go like this and they'll come from infinity and they will end over here so this is how the electric field lines look like for a positive with a negative charge two positives one negative one more negative so different diagrams you can make from looking at all these diagrams what do you feel like these field lines never ever intersect definitely they never ever intersect they never mingle with each other's Affairs they are never intersecting also they are crowding at some places they are not crowding at some other places you can also see as if these field lines itself don't love each other they try to you know stay away from each other and also you can see they hate each other so much that they never ever intersect they never ever intersect no matter what they always start from the positive charge and they end at the negative charge they always start at positive and end at negative wherever they are crowded the field is very strong whereas where they are less crowded here or let's say here less crowded the field is very very weak here also there no field lines here so the field is very weak in this region but maybe here or close to here or here the field is very very strong that is the sense that you get these are exactly the properties of electrical field lines electric field lines are hypothetical lines imaginary lines you cannot see them in reality yes you can sprinkle few things here and there and get an idea of the field lines but you can never ever see the actual field line because they are only a concept to understand other things the tangent drawn gives the direction of the field kind of makes sense also okay if I draw a tangent to this it gives me the direction of the field no two field lines will ever intersect the crowding represents the field is strong they must originate from positive and they must terminate at Negative they cannot intersect and they cannot form closed loop meaning it's not like the field lines start and end at the same point this is a closed loop this does not happen they always start from positive or infinity and they end at negative or even at Infinity because you can see over here they started at positive ended at Infinity here they started at Infinity ended at negative these are the only possibilities is that clear okay is that clear wire and other things remember we will be doing it in gos law long wires okay in gos law we will be doing those geometries not over here great now that you understand these properties I don't know why this diagram got duplicated so remember if I have electrical field lines like this if I have electrical field lines like this here it is going to be strong field here it is going to be here it is going to be a weak field and by chance somebody puts a charge maybe somewhere over here then that charge will experience tangential force and that force will be charged into the field okay along the tangent that is what it will be so using this let's do some questions coming up on your screen wow directly level two J Main's question I think we should be able to do it suppose a charge wall is already giving a uniform field now what is the meaning of uniform field you should also understand this see this one the diagram that I have drawn over here is non-uniform this is nonuniform field but imagine the electric field lines were parall to each other that means the electric field is constant this is called as a uniform field this is called as a uniform field if the field lines are just parallel and equally spaced here the spacing is not the same so now it's a uniform field the charge particle is being suspended through a silk thread and remains at a distance of 10 what is the charge on the particle this was asked this year J means 2024 Shish even if you remember the end results it's okay this end results yes it's it's going to do your job for J Mains for J Advance no hello SK talks okay thank you movie clips thank you so much thank you so much hello J Shan mugam hello J okay so let's draw the diagram first so we have electric field which is very very strong and that is 2 into 10^ 4 Newton per Kum I'm just showing it in a very dark color because I don't need to see it for a long time a Charged particle of Mass 2 G is being suspended through a silk thread and remains in equilibrium at 10 cm from the wall beware this is our wall this is our wall creating that electric field and there is a thread like so like this and this distance is 10 cm this is 10 cm the thread length 20 cm thread length 20 cm and it is staying intact in equilibrium so what might be happening think about it 100% there is an electric force in this direction that force is Q into e that force is Q into e another force is is the weight of the object and that weight will be nothing but M into G another force is basically the tension force in the string so that tension will be here these are the only three forces acting on the charged particle which is suspended and it is in equilibrium so all the forces must cancel each other okay one more thing which I would love to tell you is if I continue with this vertical line and maybe start marking the angles things will be even more apparent if I mark this as Theta these two gray lines are parallel to each other so this will also be Theta and I think I know what Theta is if I do sin Theta just check this out what is sin Theta sin Theta is opposite by hypotenuse this is 90° so it will be 10 by 20 which is half so therefore Theta is 30° so with the wall it is making 30° that's the first thing that we got good evening anime God good evening good evening Nan pum wow nice name you got okay now if this much is clear the tension will have two components the vertical component cancels the weight and the horizontal component cancels the electric for force over there so therefore can I say in the Y Direction versus in the X Direction so let's start with X first so T sin Theta right this is T cos this is T far away far means sign is nothing but the electric force which is basically QE in the y direction the T cos Theta the tensions C cos is Clos so is equal to mg I don't know the tension no issues let me divide the two so I will get sin Theta by cos Theta is Q E / m what do I need to find the charge on the particle so I just need to find Q so this will become tan Theta So Tan Theta mg goes over here and electric field comes down over here is basically the charge perfect so the charge value will be mg tan Theta M you know how much is it 2 G so 2 into 10^ minus 3 multiplied by G value which is basically 10 into tan Theta tan 30 is 1 by 3 so root3 will come below < tk3 will come below because tan 30 electric field is 2 into 10 the power 2 into 10 the power 4 perfect so what is the value of Q 2 two cancels 10 -3 into 10 will become 10 -2 10 - 6 so 1 by < tk3 into 10^ - 6 Kum which is 1 by < tk3 microc so hence the value of x should be three answer is three perfect we got the answer is that clear what is X x is what has to be found okay Hada we have to find X sir tan Theta is the uh 2K Q by mg L sir 2 k q by no I don't even have to find that K QQ by r² because this is not the electric force between two charges I already have been given the field if I know the field I can find the force by multiplying the field with the charge that's why I did not use that kums constant formula kqq by r² that is not needed because field is already given to me so I just substituted that is that okay fair enough okay Sudan both have different purposes physics Galaxy is mainly Advanced to olympiads level so it is completely Advanced to Olympiad levels okay that is what physics Galaxy's purpose is tatwa is from Basics to Advanced okay so the range only is different what exams are you targeting and what confidence you have which book you already have and what can you afford uh not uh price wise but you know confidence wise it should not happen you start with physics Galaxy and lose confidence or you should not be like you're solving dwa and you're like okay I'm able to solve uh okay initial problems are easy and I have advanced level questions also but I want to solve Olympiad then you will lack that so the purpose of the books are completely different okay right so this is done this is done let's see if you have some other question wow we have another question coming up looks complex level three question but before we head the break I think we should solve a level three question but I feel this is much easier than level two or maybe the level two should have been level three okay come on let's see if you can solve this let's see if we can solve this a Charged particle enters a point a okay it enters a point a comes out from point B maybe because of the electric field it is going in a curved path something like this okay it is going in a curved path something like I'm just showing some random thing okay this might not be the actual path Chum I'm showing some random path um the fields are in the uh vertical direction from positive to negative kinetic energy at the two points ratio will be how much okay interesting okay see guys if the field is vertical where will the force be at any point always vertical it's an charge particle okay always vertical so the electric force will always be in the direction of Y axis so if I say the force is along along y always always if I ask you what is the X component of the force the answer will be zero so what is the acceleration in the X Direction zero so what is the velocity in the X direction oh don't say zero just say it is constant just say it is constant so at this point and this point the velocities are going to have two components one is over here so this component will be like this and another component will be like this and here also we'll have one component like this and one component like this maybe so over here if you see what is the X component of the Velocity let's say it will be U cos Alpha sorry sin Alpha my bad U sin alpha y sin Alpha because if this is Alpha even this is also Alpha so the red one will be cos the green one will be S over here over here when you reach the velocity could be something else so maybe it is V maybe it is V sin beta so if this is V this is V cos this is V sin red one will be V cos so definitely these should be equal so U sin Alpha will be V sin beta so sin alpha alpha is given to be 60 beta beta is given to be 30 so therefore what do I get is sin 60 is < tk3 by2 sin 30 is half 2 two cancels therefore therefore basically V by u v by U is basically root3 what do I do with this well check this out we want KB by Ka so KB by K is half M at this point what is the speed v² upon half M at a point what is the speed it is U so m m 2 two cancels I am just left with v by U whole square but V by U is root3 so just put root3 and square it so the answer is three for this particular question which is the case is that clear very interesting question a lot of people think there is some electrostatics involved but actually more than electrostatics the concept is of mechanics and kinematics and vectors you will see electric force is always vertical so it has no contribution in the X it's like gravity gravity acts in vertical so it does not change the horizontal velocity so the horizontal velocity is constant so at this point velocity is U here it is V this is V sign this is U sign that's it so these two sign components are equal solving this we get the ratio of the speeds dividing the kinetic energies substituting you get the ratio which is required is that clear my dear Warriors is that clear okay so now before going on to electric potential we'll take a break okay we'll take a break so and then complete the remaining things so this is break time we will return we'll return at 750 p.m. okay 7:50 oh this is not 750 7:45 so 745 5 p.m. okay so uh it's 7:25 so take a 20 minute break e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e hello hello hello hello everybody let me know if I'm Audible and visible yes call all your friends message on the groups whatever WhatsApp groups friends groups yes send them message St is live and you should also share it in your status on your social media that you know Roar series is going on for all of us yep you need to put it up in your communities in your WhatsApp groups telegram groups wherever you are okay so let's begin my dear students let's begin let's begin okay just let me up the chats properly [Music] okay all right cool so let's start with the term electric potential now we are done with uh electric field we are done with electric field lines we are done with Force so potential potential energy and dipole these are the few things which are remaining now just like uh you had field around any charge there's also potential around any charge or system of charges when I say that there is potential around a charge means there is ability to store energy if a charge was placed and let me explain this to you with a simple simple concept imagine imagine you know there is a there is a teacher there is a teacher okay and uh U some coaching some Institute some classroom whatever and maybe there are some benches around that teacher maybe there are some benches around that teacher over here these are some vacant spots some batch is being launched new batch for j25 there are some vacant positions so this teacher has ability to teach some students and has some vacancies in that particular classroom so these vacancies is basically something like you know the ability of the teacher to fill up that classroom to teach those students to Mentor those students properly you know it's something like that when you actually fill up these seats with some students when you actually fill up these seats with some students Okay so so now this batch is full students are completely filled in this particular classroom then that is very similar to potential energy that is very similar to the term potential energy so same way just like the teacher replace it with you know charge or charges this is nothing but a Charged body just like the teacher you start anywhere near the charge you will have potential you will have potential that means you have ability you have ability or you are capable you are capable capable of what you are capable of gaining energy so that students which fill up the students which fill up that vacancy that point that student is like that child charge which will come over there and once that charge is there then that charge along with this charge body together will have energy will have energy and because it is of potential that is why potential potential energy that is why that system will get potential energy do you now understand the main difference between potential and potential energy potential is before placing the charge near that body potential energy is what that system gets after placing the charge potential energy has a symbol capital u potential by the way has a symbol capital V potential energy will be measured in Jewels will be measured in Jewels whereas this potential will be measured in Jew Jews per Kum Jews per Kum that is what it is everyone till this point is it clear everybody till this point is it clear yeah exactly I want everyone sad D Naran yes adika please chat in English please chat in English Okay so that even I will understand other will understand lot of telu students are there a lot of Tamil students are there imagine how it will be if telu students talking telu Tamil students talking Tamil you know Hindi students talking in Hindi how will it be it will not be good right so make sure you are talking in English and if others are also there I know you love talking in your local language but try to yeah talk in English over here okay great so potential is uh basically you know at any point is a formal way of defining is the work done to bring an external sorry a unit positive charge from Infinity to that particular Point Infinity to that particular Point that's the formal definition of it it's a scalar quantity because energy Jewels all these things are scalers they are not having any direction there is no meaning of what is the potential in that direction what is the potential in this direction no meaning at all so it is a scalar quantity SI unit is volts also you will see the other other unit is other unit is Jews per Kum both are the correct units we also assume potential to be zero at Infinity now why is this important is because see whenever you measure potential you always compare it with something like you are more intelligent or you are intelligent when I say you are intelligent that means you're comparing it with someone there is a set of people and you feel that as compared to them you know you are probably intelligent but the same person in maybe some very Toppers class might not be so intelligent he might seem to be you know not that great maybe just an average student so same way guys potential always is compared with respect to something so we assume that when you are very very very very very far away when you do not see any other charge your infinite distance away from all the things around you then the potential is assumed to be zero so Infinity is assumed to be as a standard reference point where the potential is zero so that is what has been mentioned right over here is that clear my dear students yep is it clear my dear students okay all right all right how to prepare for jmains 2024 uh impana music has asked sir can you give me tips to prepare for J Mains 2024 so I'll tell you it's very simple uh first step is you have to buy a time machine okay you have to buy a time machine then you have to go back in time at least some few months uh at least go to 2023 2023 and in 2023 watch a strategy video of how to prepare for J Mains for one year one year and then attempt the 2024 J Mains paper okay and then you will get a good college so very simple steps on how to clear jmains 2024 okay now moving ahead moving ahead moving ahead let me formally Define potential so let's say you are taking this particular Point uh infinity this is infinity at Infinity the potential is assumed to be zero this is also called as the zero reference zero reference and from Infinity from Infinity I take that charge q and bring it at this point there is some work done in this particular uh manner so that work done per unit charge is basically defined as the potential at that particular point the potential at that particular point and this work done is from Infinity to that particular point point so that's why it is also sometimes written down like this from Infinity to that particular Point DW DW DW is the small small small small small small work done but please bear this in mind this is by the external force a lot of people make a mistake here this external force all right this word many people miss that so it's the work done by the external Force upon the charge which has been brought over there till that particular point that gives you the voltage okay so this is a mathematical way of writing it this is a mathematical way of basically writing it excellente excellente very good awesome awesome okay now now once this is understood you have the electric potential due to a point charge electric potential due to a point charge which is the standard formula if you have charge Q and you are standing you are standing at a distance R from it what is the potential what is the potential at this particular point so to find that out again what is generally done is you take another test charge and you bring it from Infinity from Infinity to that particular point over here and calculate the work done and that's it you will get the potential at that particular point so the potential at that particular Point using our definition is integral DW from Infinity to that point by that external Force upon that charge so when you do this when you do this Infinity to that point the work done is nothing but the external Force external Force which is required dot dot displacement dot that displacement I can also call it as DX or Dr or whatever you want to call it upon Q and this external Force this external Force which will be needed will be k q and then small q divided by at any random point it will be basically X squ and the final limit to this the final limit to this will be basically R the final limit to this will basically be R so you calculate this work done and the formula that you get the formula that you get is nothing but is nothing but k q / k q / r k q / r that is the potential due to a point charge that is the potential due to a point charge you know at a distance of r k is kums constant Q is that charge divided by the distance where you are calculating the potential as simple as that okay so this formula again very very useful for all of you for solving many problems in fact in fact you will find problems like this where you might have multiple charges q1 Q2 Q3 Q4 Q5 q6 Q7 like that and due to each charge there might be a potential at this point so when you multiply sorry when you add the potentials due to all the charges potential due to this charge potential due to this charge you add them you will get the total potential at this point and the best part is you don't have to worry about the direction you potential is a scalar quantity so the best part is you just simply add their magnitudes with the signs of course some of them might be positive some might be negative so you add them with the signs you will simply get the voltage at that particular point so this is again an extension of superp position remember if this was a problem of electric field then each field will be in different directions you had to do the vector sum to find the net electric field but for potential that's not the case you just have to Simply add the values of the potentials is that absolutely clear is that absolutely clear yes everyone with me great now also keep this in mind also keep this in mind it is quite possible that at particular Point number one you might have potential one at other point you might have potential two and then and then between these two points you will get the thing called as the potential difference this is basically your potential potential difference potential difference potential difference and very very important is it doesn't matter which path I take whether I go by this path or I go by this path really doesn't matter is independent of the path is independent is independent of the path and why is it so whether you go this path number one or path number two is because since electric field is conservative in nature electric field is conservative is conservative in nature and conservative forces have that property that you don't have to worry about the path as long as your initial and final path points are same no matter how you reach the destination as long as the source and the destination are same the work done will be the same so potential difference will also be the same so potential difference will also be the same so this is something which you need to know also keep in mind the units of potential where is it coming as uh you know Jewels per Kum and all of that so if I do one Jewel of work one juwel of work to bringing a charge from Infinity to that point in bringing one of charge and bringing one Kum of charge the voltage at that point is set to be 1 volt the voltage as that point is set to be 1 volt that is why you will see 1 volt is one Jewel per Kum that is how it has been defined so if I do one juwel of work in bringing 1 Kum of charge from Infinity to that point then at that point the potential is 1 volt that is what the meaning of this statement is is that absolutely clear okay so these are some important things regarding potential so I think it's a good time that we start with some questions as on the screen a cube of side B has a charge Q at each of its vertices determine the potential and the electric field due to this array at the center of the cube one of the answers is easy one of the answers is lengthy can you think and tell me which answer is lengthy which answer is easy in this it's a cube after all let's think about it Cube all right this is the cube and where are the charges the charges are on the the charges are on the each of the vertices so there are remember eight viices all the eight VES the charges are there all the eight VES the same charge Q is there and the side length and the side length is uh B side length is b so if you are at the center of the cube the center of the cube is somewhere here try to visualize that the center of the cube will be somewhere over here so basically just try to draw the diagonals probably that will make it very easy for you to understand so I'll just try my best to draw the diagonals somewhere over here yeah so if you draw all the diagonals you can see where it is meeting so that is basically the center that is basically the center of the cube are you able to visualize this are you able to visualize this yep so now think and tell me yes which of them is easy potential is easy wrong field is easy field will cancel in fact the electric field is answer is big fat zero where is it the electric field yes this one will cancel all the fields will cancel all of them will cancel due to all of them hence the net electric field will be a big fat zero that's the direct answer because of this charge and this charge opposite opposite opposite opposite opposite all opposite charges the fields will cancel the main problem is with the potential and the good part about the potential see I know it is little L but the good part is first of all it is scalar so I just have to worry about the magnitude that's it number two this point is equidistant from all the vertexes this to this this to this this to this this to this so if you take any diagonal so my dear students if you take the diagonal and this point is at the exact center like you can see what is the length of the diagonal what is the length of the diagonal the diagonal length the diagonal length of any cube is basically the side length is basically the S length time root3 the side length is b so it is bot3 if that is a diagonal what is the distance between this Green Dot and the blue dot what is the distance between that Green Dot and that blue dot let's say I call it as D that distance D is a diagonal divided by divided by two it's exactly the midpoint it's exactly the midpoint so it will be B divided by B / 2 and this is root3 why is that important is because the charge that you are talking about Q is over here here and so many other places and you want to find the potential at this point due to all the charges so when I try to find the total potential it will be there are 1 2 3 4 5 6 7 8 eight charges into potential due to each charge so it will be 8 * k q divided by this distance which is D this distance which is basically D so it will be 8 k q divided by distance which is basically B otk 3 divided 2 so that two gets multiplied so it will just become 16 k q divided by divided B < tk3 that is the answer 16 KQ by B < tk3 16 KQ by bk3 exactly the same thing and the field value will be zero the field value will be zero perfect we got it yes is that clear everyone everybody clear awesome awesome keep this in mind okay everyone clear about this everyone awesome CH let's go to the next question coming up on your screen then let's go to the next question coming up on your screen okay CH let's what is it wow electric potential J means 2023 question electric potential at the center of the two concentric half Rings we did a question on half ring but that was on the field now they have asked a question on the potential interesting question is what is the potential at the center Lambda are the linear charge density Lambda is the linear charge density okay capacitance in a separate chapter capacitance is going to be in a separate chapter see guys first of all let me tell you one thing when you have a semicircular ring and you want to find the potential here the best part is all the charges on the ring are at the same distance and I don't have to worry about the dime sorry the directions so if you take any charge it's at the same distance so when I try to find the total potential which is summation k q divided by divided by the radius K and R are constants they will come outside I will just have summation of the charges which is basically the total charge on the ring which is basically the total charge on the ring but if I write it in terms of Lambda remember Lambda is how much charge is there per unit length how much charge is there per unit length the charge on the ring is capital Q the length is the semicircle circumference which is pi r not 2 pi r 2 P is for the circle so that is Lambda so rearranging this I will get Q is equal to uh Pi Lambda R substituting Pi Lambda R over here so I will get k / r instead of q i putting Pi Lambda r r r will get cancelled and I will have K Lambda Pi K Lambda Pi if you want I can substitute the value of K also it will be 1 by 4 Pi Epsilon Lambda Pi Pi Pi by by so I will just have Lambda Lambda by 4 Epsilon KN Lambda by 4 Epsilon KN is the potential due to a semicircular ring this deration I will have to do on the spot in the rough book without that I will not be able to do okay so now going back to this there are two rings oh the best part it is independent it is independent it is independent of R1 or basically R the radius so means this R1 and R2 is useless that's why you see in the options it's not there number one number two in the question it is not given so that's the best part about it so when I try to find the total net potential potential due to ring one plus potential due to Ring 2 just go to this formula Lambda by 4 Epsilon Lambda by 4 Epsilon both have Lambda only so Lambda by 4 Epsilon 1/4 + 1/4 is half so Lambda by 2 Epsilon not which is option A let's check it out yes uh or no yes it is the correct answer it is the correct answer Lambda by 2 Epsilon is that clear my dear students yep shall we go ahead shall we go ahead to the next one okay let's go let's go let's go let's go let's go let's go what do we have electric charge is placed g means 2024 this year uh is placed at the origin and two points are situated and so and so the difference of the potential between p and Q is okay let's understand this p and Q X and Y AIS we'll need this is X this is y p is < tk3 < tk3 so this is < tk3 < tk3 and Q is uh Root 6 0 so Q is basically otk 6 comma 0 question is what is the voltage difference between these two points to find that first what is the potential at Point p we need this distance so if I find RP RP will be root of < tk3 s + < tk3 S which is 3 + 3 which is 6 otk 6 if I ask you what is this distance RQ well that is directly Root 6 oh wait a minute RP and RQ are same so RQ is equal to RP which means the voltage at Point P will be equal to the voltage at Point Q so if you ask me what is the voltage difference between the points p and Q the answer will be a big fat zero which is C let's check it out yes it is correct the answer is going to be C because the distances are same the distances are same is that clear everyone shall we move ahead loving the session understanding potential we are solving all kinds of questions varieties of questions just for you when you talk about a Charged ring and you want to find the potential this job is much much easier for a ring for potential because you don't have to worry about the direction because you don't have to worry about the direction my dear students so if you take any charge on the ring from that point where you want to find the potential this distance of r² + x² is same same for all charges on the ring all charges on the ring if I call this as small R and if I call the charge over here as DQ then at this particular point then at this particular point when I try to find the voltage it will be integration of all the small small voltages due to all the small small DQ charges so each DV each DV will be K DQ divided by the distance which is basically R but K and R are same for all the charges so bring that R outside and what remains inside the integral is just DQ DQ's integration means I'm summing up all the charges here which is just going to be capital Q and this comes over here as it is as it is that's it so it is KQ divided by small R but small R is that one that formula which I have just substituted here so hence the total voltage will be k q / otk of r² + x² so this is the formula this is the formula for a ring which is charged to find the voltage voltage to find the voltage KQ /un r² + x² is this clear understood why is it simple is this simple okay very good very good all right all right now yeah this is done now we have to go to uh electrical potential energy so let's go to electrical potential energy now we have done with potential so let's start with potential energy uh so what is potential energy electrical so imagine imagine this is your Universe which you basically can also say that this is infinity this is your universe and this is like a playground and all the players are outside the playground the playground is the universe to get the players inside the playground you need to pay a lot of money to them correct only then you know IPL auctions they will play on the ground or else they have no motivation so same way imagine there are many charges many charges 1 2 3 4 Etc q1 Q2 Q3 Etc Q3 q1 these charges right now are completely unaware of each other because they are outside the universe they are so far away outside means very very far away they don't know they exist it's like you're far off relative your mom's um you know uncles Sons uh you know again some daughter-in-laws some cousins mothers Brothers something something you don't even know they exist now you bring all these family members together you bring all these cricketers on the playground and eventually you place these charges q1 Q2 Q3 Q4 like that over here you have assembled them like a family gathering somebody's wedding is there all these family relatives everyone they have come together for that particular function they have assembled you have arranged them you have arranged them to together okay they're all interacting with each other oh hello you know what I'm that M that you know that fathers this Sons this brother this cousin this daughter-in-law blah blah blah blah they're interacting with each other so when you do this process you have done some work that work done to assemble them is called as the potential energy very simple so potent electrical potential energy by the way the symbol is uh capital u is nothing but the work done to Simply assemble the charges assemble the charges that's it assemble the charges and this is nothing but integral again DW but do not divide by any charge just Infinity to the points or the location where you want to keep them from Infinity to the location where you want to keep them also bear this in mind when the separation is infinity it is assumed to as zero they have no potential energy when they are really really far away that is also termed as the zero reference zero reference that is called as zero reference energy that means they do not know the other charges exists and their energy is taken as a baseline as a reference as zero you compare everything with respect to this you compare everything with with respect to this particular potential uh energy okay so this is the true way of defining potential energy when you divide it with charge what you get is potential when you divide it with charge what you get is potential exactly okay yes surwa contains J means pyqs in a separate exercise J advanced pyqs in a separate exercise okay I hope this is clear h okay okay CH let's let's continue if now you happen to take two charges what is the energy of such a system to assemble them so it's like only two people it's like pandu Champa before me pandu Champa never existed or pandu did not know about Champa Champa did not know about pandu but thanks to your s sir pandu got to know about Champa Champa got to know about pandu so charge one and charge two were really far they got to know about each other they were brought together and to assemble them I did some work that work is K q1 Q2 by R that work to assemble them together is K q1 Q2 ided by R so then you might be wondering sir what if there are more charges well the answer is very simple let's say there are three charges then what will happen these two will have energy k q1 Q2 divided by R12 these two charges will have K Q2 Q3 divided by the distance R23 these two charges will have K q1 Q3 divided by the distance between them which is r13 perfect so now what if what if there are even more charges even more charges well answer is simple you find the energy with this energy with this energy with this energy with this energy with this energy with this energy with this with this with this with this with this what else is there even this even this uh even this all this basically all combinations that's all so whenever there are multiple charges the potential energy of the system the potential energy of the system is K Qi QJ QJ q1 Q2 Q2 Q3 Q4 Q7 Q8 Q5 Q5 Q3 Q2 Q7 like that divided by the distances between the respective charges but the summation of that so that's why I will have to put a symbol over here I'll have to put a symbol over here like this but the catch is I should never be equal to J I should never be equal to J so you try out all the combinations okay I should never be equal to G as simple as that we should not repeat it is that straightforward my dear students yeah so for the exams would it be better to solve pyqs or in ncrt isan for J it is better to solve pyqs not ncrt inext ncrt inext is okay for cbsc level but for J level don't go with ncrt inext you have to go much more beyond that it's of no use even for neat these days just solving ncrt index questions is of no use there are couple of cases where they use those questions but that is very few not like out of 50 Questions the 40 questions are from there from 50 questions maybe two or three questions might come from there maximum that two after changing the values so pyqs is a better option not ncrt in text okay so now that you know about this now that you know about this let's go ahead and solve some questions three particles each of having 10 microc colums are placed at the corners of a triangle the electrical energy of the system is how much let's draw a triangle first let's draw a triangle first and three particles are there three particles are there of 10 micrum 10 micrum okay 10 micrum and the corners of side 10 cm so the side length is 10 cm question is find the energy of the system now when I try to find the potential energy of the system understand there will be three terms this guy with this guy this guy's energy with this guy this guy's energy with this guy so there will be three terms and the best part is all the charges are equal the distances are also equal so I will have three times the energy between each pair of charges three into what is energy between each pair it will be k q q divided by distance Square no distance only no Square so it will be 3 into K is basically K is basically 9 into 10^ 9 charges are 10 Micro so 10 into 10^ - 6 two times so Square divided by the distance which is 10 cm which is basically 1 which is basically 0.1 so my dear students what will happen 93 are 20 27 that's it 27 into all these other terms just check it out what will it be 10 to - 6 into 10 will make it 10 ^ - 5 whole Square will make it 10 ^ - 10 - 10 into 10 ^ 9 will make it 10 ^ minus1 which is 0.10.1 and 0.1 will cancel so just check this out this will become 10 ^ 9 into 10^ minus 10 divided by1 is 10^ minus 1 this whole thing will just become 27 whole thing will just become 27 which is option C yes that is the correct option very good Dakar adika awesome hello Supra I'll watch your class recorded no issues ruika I'll be starting current electricity after one more week next week gos law Motion in Wy after that current electricity make sense okay cool shall we go ahead shall we go ahead to the next question on your screen two charges are fixed as shown and a particle of some mass is released here and it is you know on a frictionless plane this is a horizontal plane it's not vertical gravity has no effect find the speed as it reaches the origin it's interesting problem if you notice see this charge Q2 and this charge q1 are how much q1 and Q2 both are positive both are basically positive so let's put it over here this is also positive and this is also positive charge both are 2 micrum 2 micrum then you have a negative charge over here how much is that it is min -4 micrum so this will be attracted by both of them it will accelerate and after some time this charge after some time you will see that this particular charge would have you know achieved some speed as it reaches over here as it reaches over here at the origin so the question is what is that particular speed so think of it this way when it was here it had no kinetic energy when it is here it has some kinetic energy where did it gain that kinetic energy from it can only come from one thing electrical potential energy so maybe here there was some energy here there was some energy that energy has been differred by some value maybe potential energy was lost and that's why kinetic energy has been gained so just use energy conservation so if I use simply put energy conservation energy conservation initial potential energy plus ini IAL kinetic energy is final potential energy plus final kinetic energy initial potential energy think about it think about it my dear Warriors think about it my dear Warriors what that initial potential energy would be this charge with this charge this charge with this charge by the way this is minus three this is four so obviously this is 5 m this is also 5 m so the energy of this guy with this guy energy of this guy with this guy will be how much just check this out it will be K Q2 Q3 which is I will call Q2 and q1 as q that will be better q1 and Q2 okay I'll just call it as Q guys that will be better so Q into Q3 Q into Q3 divided by that distance which is basically five but there are two such charges this with this this with this so into two times into two times now another energy is also there between this guy and this guy but I will not count it reason because when I complete this equation and I write kinetic energy is zero because here it was at rest of course and I write energy again over here understand that these two charges will still have the same energy these two positive charges will still have the same energy whatever is the energy between q1 Q2 will remain the same only this charge is moving so if I put it here I'll put it here they will anyways get cancelled so for the sake of your understanding I'll just put it over here plus K Q2 Q3 Plus K Q2 Q3 both Q2 Q3 I have assum Q2 q1 sorry it is assumed as Q only so K QQ divided by the distance that distance is going to remain the same so don't worry only about it don't worry about it kinetic energy initially is zero this is equal to final energy final energy again these two charges will have the same energy these two charges will have the same energy so k QQ by D do you notice that this term anyways gets cancelled anyways it gets cancelled anyways so now when you reach here when you reach Here My Dear students this charge has come over here this Q3 charge has come over here what is the energy between Q3 and Q2 Q3 and q1 well that will be K Q3 into Q2 Q2 and q1 both are Q so Q into Q3 divided by this distance which is basically three but this energy and this energy two separate this with this this with this so into two times and it also has kinetic energy so half M v² and half M v² so that is the kinetic energy potential energy is this but this part and this part anyways gets cancelled do you understand it yep at the beginning what to do for solving the problem Karthik analyze what is happening why is it moving which law which theorem which property which uh conservation what will help you here I understood that because it is accelerating and it is gaining some energy forces will be difficult because force will continuously change the angle and the magnitude energy will be easy because here the gain of the energy kinetic wise is coming from the difference of the potential energy so initially there is some potential energy of this entire system one term one term one term three terms are there two terms here and this is the third term finally when this charge comes here this with this this with this and these two with each other so again three terms one and two terms over here that is final initially it was at rest so initial kinetic energy zero final kinetic energy half MV s that's it after this it's purely just substitution of the values it's just pure substitution of the values K value you'll put it as K value you will just put it as 9 into 10 ^ 9 Q value you will put it as 2 micro so 2 micro Q3 Q3 Q3 Q3 Q3 is how much Q3 is 4 Micro 4 micro but it is with a negative sign but it is with a negative sign the whole thing divided by the distance is five okay and multiplied by two and this is equal to all these things over here all these things over here K is again 9 into 10^ 9 qq3 qq3 is 2 micro into -4 2 micro into -4 micro whole thing divided by the distance plus half into mass mass is how much 1 G so 10 ^ minus 3 into v² solving this you will get the value of v² and then you will get the value of V which comes out to be at 6.2 m/ second 6.2 m/ second that's is a very good question that's why it's level three this is level three question understood how to solve it yes this is Advanced that's why level three it's ADV once that's why level three I hope this is clear mesu it will be for more 1 hour expect it for more 1 hour okay now let's come to another interesting thing before we go on dipoles before we go on dipoles okay and that is the relationship between the field and the potential this is another very very very important thing one thing you would have understood any charge around it creates field any charge around it also creates potential so if a charge is able to create potential and field why won't they be related to each other just like this diagram over here shows some system of charges you can see some positive and negative charges you can see these lines these curved lines are those electric Fields going from positive to negative and those shaded regions is basically the potentials at different points so the potentials and the fields are actually related to each other that is what I want you to realize whenever whenever you take a let's say positive charge probably show to you here whenever you take a positive charge you will see that around it around it I have regions where the potentials are same because at the same distance voltages are same all these points are equ potential I can go real far Also let's say over here at all these points again the potentials are going to be the same I go even a little bit more far again at all these points on this big circle you will see the potentials are going to be the same these are all concentric circles and here I can call the potential to be V3 here it is V2 here it is V1 all these points same potential all these points same potential all these points same potential so these are called as equ potential lines or surfaces equip potential lines or surfaces on the equip potential lines or surfaces the potential Remains the Same the potentials Remains the Same so I can also have I can also have the equip potential lines looking probably something like this I can also have the equip potential lines looking something like this this is V1 this is V2 this is V3 and so on and so forth okay so I can have equip potential lines looking like this V1 V2 V3 Etc if by chance if by chance I go from this point to this point understand I'm on the same voltage line so the voltage difference will be zero voltage difference will be zero but but if I happen to jump from this point to this point doesn't matter which path I take then definitely there is a voltage difference the voltage difference will be V3 minus V1 final minus initial I've gone from here to here so there is definitely a potential difference there is definitely a potential difference I hope that is clear not just that you will also notice that if I happen to SU superimpose if I happen to superimpose the electric field lines meaning this is the this is the electric field line electric field line so many more field lines will be there uh let me show it like this these are basically your electric field lines you will not notice that these electric field lines no matter where they are they are always perpendicular to the equip potential lines are you seeing that no matter where you go no matter where you go they are perpendicular to the equip potential lines so on the same diagram if I happen to show the electric field lines I will have to drop it perpendicular to the equip potential lines I will have to drop it perpendicular to the equip potential lines maybe you know it is a little difficult but maybe it is like this this is how the electric field lines might look like always always always perpendicular always perpendicular so the electric field lines electric field lines are always going to be perpendicular always going to be perpendicular to the equ potential lines equ potential equip potential lines this is a very very important property which you will see very very important property which you will see not just that thank you thank you vantu conqueror glad you are liking the vbody classes another important thing another important thing about the electric field lines is that notice as we go far away the potential reduces from this positive charge electric field is going from higher voltage to lower voltage to even lower voltage so here also if I'm going like this that means V1 is more V2 is less V3 is even less so always electric field always electric field will travel electric field lines will always travel from high potential high potential high potential to a lower potential to a lower potential this is always a fact all these properties you definitely must know okay all these properties you must definitely know is this point clear everyone okay it makes sense also if you're at a high voltage obviously the field will bring you to a lower voltage lower potential and there will be a voltage difference created okay if you go along the same field sorry potential line then there is no voltage difference at all there is no work done at all because potentials are same only when you jump the potential lines will you see the voltage difference occurring there another important thing yeah clear very good excellent day excellent day now if I am jumping from one voltage to the other voltage via some random path just like over here I'm going like this taking a charge particle understand there will be also work done to take that charge from here to here work done to take the charge from here to here there will be also potential energy which will differ just like at this particular Point number one the energy would have been the potential at that point the potential at that point which is uh basically V1 V1 into the charge into the charge okay that is the potential at that particular potential energy at that point how because potential is Jews per Kum into the kums will give me the Jew of energy Jews perum into the Jews will give me the Jews of energy there similarly at this particular Point number two the energy at that point the energy at that point would have been the potential at that point multiplied by the charge so think about it if I subtract U2 With U1 If I subtract U2 minus U1 basically Delta U it is nothing but U2 minus U1 what will I get what will I get think about it that charge which is there it will be common that charge which is there it will be common and what I will have is vs2 minus V1 what is vs2 minus V1 it is the potential difference this is nothing but the charge that's it that is going to give me the energy potential energy change that is going to give me how much has my potential energy changed that potential energy where will it come from who is going to change that energy somebody has to do some work so this will come from some kind of external work this will come from some kind of external work keep this in mind very very important also bear this in mind back in 11th standard or you will study it later on that change in the energy is also technically is also technically the negative is also technically the negative of the work done by electric force this is way different electric force is that internal Force the electric field which is doing the work external is somebody else pushing it so this is negative of that this is something which you have learned long time back in work power energy chapter Delta U is negative work done by conservative Force so electric force is that conservative Force now this statement is so important and also so confusing because many students often make mistakes over here often make many mistakes over here so let's try to do a question so that we are you know understanding the concept really well let's say for example sake a two two Kum charge a 2um charge is taken as shown is taken as shown find find the work done by the external Force work done by the electric force the potential difference and the potential energy difference and the paths are as follows so this is - 10 Vol and this is 30 volts okay plus 30 volts so this is what it is and uh you have taken the charge from here via this particular path okay to over here this is how you have taken that uh how much two Kum of charge two gum of charge so let's try to solve this particular question come on first things first tell me quickly what is the potential difference that is the easy part final minus initial always final minus initial vs2 minus V1 that is 30 minus - 10 so hence the answer should be 40 volts just check that out voltage difference is 40 volts everybody with me okay very good next important thing is the work done next important thing is the work done and the energy difference so let's try to find out how how much is the energy difference the energy difference will be charged into the voltage difference as per this formula Delta U is charge into the voltage difference so let's try to find it charge is two voltage difference 40 so it will be basically 80 jewles so the energy difference is 80 Jew next thing what is the work done by the external force it is always a Delta U so hence that external forces is work done is also 80 Jew external Force has done 80 Jews of work what about the work done by electric force it is negative Delta so it has done minus 80 JW so that also we found this is how you solve these questions I hope after this at least the sign you will not confuse and you know what is what okay everyone till this point clear this is one of the most easy but important problem see some problems are easy but you know what in the exam you will always if you don't understand it properly you'll always get confused what was negative what was positive who is multiplied by whom etc etc so I have explained this to you very very clearly also the properties of electric field lines with respect to equip potential lines now there is a Formula which relates both of them electric field and uh this thing it go something like this say guys your force or rather do it like this the change in the uh potential energy is negative work done by the conservative Force so that work done I can say it is f into displacement that conservative force that conservative electric force into the displacement therefore we get the conservative force is minus du by Dr you would have seen this equation even in work power energy chapter now what I will do I will divide this energy with a charge and this Force also with a test charge if I divide force with a test charge what do I get obviously Force per unit test charge is nothing but field and what do I get if I divide energy with charge just go back over here if I divide energy with charge I will get voltage difference energy Q if I bring it down I'll get voltage difference so hence this should be nothing but DV and this drr remains as it is so this is a very very important relationship electric field is negative rate of change of voltage is negative rate of change of voltage with distance as simple as that sometimes that DV byd is also called as a voltage gradient so it is also called as negative voltage gradient voltage gradient okay so field so electric field so electric field electric field is negative rate of change of voltage as simple as that that is what it is yes bakar very good kalami every day 5:00 classes on weekday Monday to Friday okay you will have classes is that okay Monday to Friday correct moving on moving on to some questions but before I show you the questions let me tell you a very simple example let's say if I tell you let's say if I tell you the voltage is X Cube can you find me the field what you will do is you will just say electric field is minus DV by DX because voltage is a function of X so it will be minus derivative of x Cube X Cub's derivative is 3x² that's it so electric field is min - 3x s so if the question demands can you also find the electric field at X is equal to 2 m then you'll just substitute it over here so electric field will be minus instead of X you will put 2 square so 2 so it will become 2 square which is 4 4 3 is are 12 so - 12 volts per meter or Newton per Kum whatever you want to use so that is the electric field value is that okay that is how we'll solve those kind of questions can we differentiate voltage with respect to R to get whe uh field yes that is what we have done diaka we have differentiated the voltage with respect to the distance to get the field exactly what we have done but with a negative sign that's all okay so let's try to solve this let's try to solve this particular uh question over here let's say if I put a question like this electric field no not electric field voltage voltage is let's say x² plus y - 3 can you find the field can can you find the field that is the question can you find the field that is the question now there is more X as well as y in the equation so that becomes a tricky part that becomes a tricky part yeah yes sir work done is equal to minus du work done external agent field always that work done is of the field or the conservative Force who is that Kara Sharma Kar Sharma that is of always the conservative Force so this point where is it yeah do you see this work conservative conservative means who are the conservative things who are those conservative things conservative is like gravity spring electric like that okay always this is for conservative forces work done only so this Force conservative Electric Force spring Force gravitational force so in this case we are referring to electric force so that's why that Force divided by the charge will give me the electric field if it was force by mass it would give me gravitational field okay that's what it is okay let's try to solve this question let's try to solve this question what to at the beginning what to do to solve the problem yes Ki so first of all because you can see it is a relation in X and Y both so we'll separate differentiate X and Y okay and then find each component separately see think about it if I just have to find X component I just have to differentiate the voltage with respect to X if I have to find the Y component obviously I'll just have to differentiate it with respect to Y and everything else is a constant so now when I differentiate it with respect to Y what is that x² + y - 3 think about it X is going to be a constant rate of change of Y not X X is not changing only Y is changing so when I move along why why will X Change X is a constant so treat it like a constant just like that number three treat it like a constant just like this number -3 so it will be 0o plus just the derivative of y with respect to Y minus again 0o this is zero this is also 0 Y is derivative with respect to Y is 1 similarly over here when I differentiate it with respect to X which is x² + y - 3 I'm differentiating with respect to X so X is changing Y is a constant just treat it like a constant so it is just the derivative of x² this is zero and this is also zero so X Square's derivative is 2x so this is X component this is the Y component so the final answer of the electric field will be X component did I miss that minus sign somewhere yep yep okay and did I miss the minus sign here yes definitely so this was also minus so this is minus okay perfect now it is okay all right so electric field will be Min - 2x this is X component so I the Y component is minus one JC so minus jcap Newton per Kum that is the answer is that clear how to solve this is that clear my dear students so this this particular part 2x that was your ex component and this particular part over here that was your e y component that is how you solve these questions cool everyone yeah as if you can do one thing very simple just search for over here basic maths basic maths okay not this maths this is that maths uh I have done this do this before studying 12th okay you can study that also where is yeah this basic maths this is basic maths in physics quadratic and algebra this particular uh you know lectures are already there you can use that but if you still feel that okay sir I'm not able to understand leave comments I will see if there are more comments then I will definitely take it up for all of you is that okay shall we go ahead cool okay yes for external agent kushara you can write work done is equal to plus du in fact that is what I have written also Kara let me just show it to you that is what I have written also see this work done is plus Delta U for external for internal basically electric force I have written Delta U is minus work I have written it already whatever you are saying I have already written it down properly so I mean these notes now you keep it with you in your notebook in your short notes whatever because I'm making this slides with lot of efforts with all the colors everything so that it registers in your head properly okay cool shall we go ahead all right let's go ahead let's talk about dipoles now let's talk about dipoles what is this dipoles die poles D is basically Two Poles is basically polarities polarities polarities are positive and negative polarities are positive and negative so when you have two equal but opposite charges two equal but opposite charges separated by a small distance separated by a small distance then then that is called as a dipole then that is called as a dipole this dipole also generates something called as a dipole moment which tells you the effect of that particular dipole which it will have on its surroundings maybe the field and the potential so say for example you take a negative charge and a positive charge like so and there is some distance between them let's say I call it as L let's say the positive charge is plus Q the negative charge is minus Q then there is a dipole moment which is formed from negative to the positive side be very very careful I'm repeating again not from positive to negative because see electric field will go from positive to negative dipole moment is a vector which has been defined from negative to positive this is your dipole moment this is your dipole moment P so dipole moment dipole moment is always always is always separation separation multiplied by any one of the charge any one of the charge that's dipole moment so magnitude wise the dipole moment will be either you take this charge or that charge just the magnitude of it just the magnitude of it and multiply it with the length separation which is L that's it that is basically your dipole moment that is basically your dipole moment M the unit the unit of this particular Dior moment separation is in meters charge is in Kum so it is basically Kum meters it's not centimeters CM it is not centimeters it is Kum meters now what is the problem is that when you see your ncrt books and all you will see this number as 2 and then this 2 I mean why would you do that I mean I understand that later on you might have to BCT it and you measure it all the distances from the center of the dipole but for that alone reason writing it as 2 L is very very misleading imagine I ask you what is the distance between you and uh your home and the school and you say Sir the distance is uh 2x where 2x is equal to 500 M and then you are like X is the distance I'll be like why are you saying 2x is equal to 500 where X is the distance between my home and the school why can't you just say it is 250 M right so that is the point so no need of writing that 2 I'm repeating again no need of writing 12 if you are using 12 then use 12 everywhere and know what that 12 means 2 is the total distance L is the midpoint to the distance till the charge that will create unnecessary confusion for all of you yes correct in all my lectures I'm saying this looks like Dakar who is it Dakar oh Dakar has been following all my lectures what else should I say differently because this is a common mistake and every year people do the same thing okay and what is the direction the direction this is a vector quantity by the way it's a vector quantity and that Vector quantity's direction is always from negative negative to positive negative to positive it is negative to positive very very important thing all right so this is a dipole moment which is charge into length unit is Kum meters and uh yes yes you can see negative to positive charge oh see here also somebody has written 2 a because this is how it is written in ncrt okay so a and a not needed you can just write it as L who cares about that 2 all right so let's go and solve some questions do we have a question yes system of two charges QB and QA separation is is given by the coordinates how much charge is given is also there printed find the total charge and find the dipole moment extremely straightforward problem of level one very good thakar thank you karian if you are facing difficulty in solving problems just check my first of all yesterday's video have told some three-step approach of solving the question questions how many questions you need to solve per chapter also what is the approach of any chapter to be completed most important thing don't focus on too much of note making focus on watching the lecture reading minimal and maximum time problem solving in that problem solving 50% time believe me goes in just you know the basic problems solved examples uh you know below average questions and all that the remaining 50% goes in solving Advanced questions pyqs and more difficult above average questions so that first 50% time is the most difficult time so if you are able to if you are able to systematically improve your level right from the basic to the highest level and that happens with a proper textbook or basically a proper problem solving book you start from level one level two level three level four then you will get the that confidence and you have to spend a lot of time practicing the same problems again and again solving at least two to four questions of the same model watching a teacher solving those questions again and again only then you will get adequate confidence to solve the questions thank you thank you love physics for all the love from uh from Kerala thank you thank you okay so my dear students over here what is there the distance of separation how much is this this is 15 this is minus 15 so that is 30 cm obviously which is3 M and the dipole moment will be charg charge charg 2.5 10^ minus 7 into. 3 3 you take it here so it will become 7.5 into 10 ^- 8 Kum meter 7.5 into 10us 8 how many of you wrote it yes very good but what is the direction uh a is positive this is positive B is negative so always from negative to positive so it is downwards so dipole moment Vector form will be 7.5 into 10 ^ minus 8 downwards meaning minus K hat and this is Kum meter this is the correct way of writing it minus K you see this minus that is exactly this minus K hat exactly and one of the other question was the total charge obviously the total charge is going to be zero because there is equal amount of positive and negative there is negative and positive so the total charge will be zero very good moving on to the next one three charges are arranged at the vertices of an equilateral triangle as shown in the figure find the dipole moment of the combination find the dipole moment of the combination come on now you might be wondering where is the dipole sir where is it well well well I'll tell you you can break this system into two dipoles how I'll show it to you don't worry see there is one negative charge here fine there is another negative charge here fine but there is two positive charges here split it one for each negative charge one positive here one positive here now you will notice one interesting thing now you'll notice one interesting thing that there is one dipole which is formed oops not that great but yeah one dipole which is formed like this and one dipole which is formed like this both the dipole moments are magnitude wise same magnitude wise P2 is equal to P1 obviously but they are inclined at an angle of 60° with respect to each other so now you have to find the net dipole moment meaning the vector sum so the net dipole moment can be found by root of P1 s + P2 s + 2 P1 P2 cos what is the angle 60 that's it P1 P2 both are same so just take P outside or P1 outside so what you will have is 1 squ + 1 s + 2 into 1 into 1 into 1 into 1 into cos 60 which is basically half 2 two cancels 1 + 1 + 1 is 3 so P1 < tk3 but what is P1 P1 is dipole moment of any1 so it is Q into distance what is the distance D so QD < tk3 so that is the net dipole moment that is the net dipole moment QD root3 how many of you got it no not root2 it is root3 root3 so tomorrow I have unit test in my Institute physics portion is electrostatics potential and capacitance I already solved some 200 questions in IC but feeling nervous J happens because this is a year start and first chapter and the main problem is when you are starting your year first uh sorry when you're starting your year academically 11th or 12th you want that the year should start really good and you feel that if it does not go well then you know I might not understand anything in the next few months or you might feel that I am not that great or I had practiced so much or I had put in so much of sincere effort right from the beginning and all this has happened at the first test only so you know be prepared for anything I mean things might go bad things might go well so if it goes well don't be very overconfident that is also bad and if things don't go uh as expected then you need to understand what else has happened what was the mistake that you did so it's a part and parcel of your life and you might have lots of ups and downs in the next few months don't worry but what matters is if you study these topics properly it will be very easy for you if you do not lose your cool in the end after September October to revise all these things and score really well in the full syllabus m test there are many students who do very bad in the class tests unit test but do very well in the final test it happens every year okay and if you maintain the consistency students who do well in all the unit test obviously they do much better also in the final test okay but if you are too confident initially then you might also go down don't worry you will do well all right cool so let's let's yeah root3 QD that is the answer moving on to the next one electric field and potentials due to the dipol so let's see what this is I have made a beautiful slide wow such a beautiful slide isn't it okay this is going to come as printed slide for all of you soon but uh first let's understand what does this mean okay and which side have I shown okay H okay that is supp all right so let's use the same sides so that it looks less confusing okay so we have a negative charge we have positive charge okay and some distance between them and the dipole moment is like this of course this is the dipole moment let me create a duplicate of this if I ask you how the electric field lines look like and how the equip potential lines look like so let's start with it electric field lines will look something like this this is approximately how the electric field lines will look like very very approximately right these are your electric field lines okay I just put it over here electric field lines similarly there will be also equip potential lines remember equip potential lines will be just perpendicular to the electric field lines so if I just happen to show them first perpendicular the most important perpendicular if I show it it's something like this it's over here exactly you know bisecting both of them you know what is so special about this line it is equid distance from the negative and the positive charge so actually it is a Zer volt equip potential line so actually it is a what 0 volt 0 volt equip potential line because it is equidistant from negative and positive charges so both of them will have the same effect but of the opposite side if you go this side it is more positive if you go this side it is more negative so if you show other field sorry other equip potential lines probably it will be like this then probably even like this it's got to be a little bit difficult to draw but still I'm trying my best these are the equip potential lines looks very scary at first looks like some insect or something okay these are your equip potential lines so do you see that are you able to visualize it loving the diagram understood Yep this sides are more positive potentials positive potentials because you're closer to the positive charge positive potentials on this side you will have more negative potentials because you're closer to the negative charge as compared to the positive ones see anywhere here you're closer to this than to this that's why you are more negative this is how the electric field and the electric potential lines look like now this is diagram fine but if I want to find Value I can draw a diagram and expect to get the value right so let me just duplicate this I need it now imagine I want to know the electric field or electric potential at any point I want to know the electric field and electric potential at any point so imagine I just from the center I go anywhere some random point it could be here here anywhere some random point this is at some distance R from the center at this particular point if you notice if you notice if you notice the electric field you can see it is going like this so the electric field is in this direction you can see this is how the electric field is and at that particular point at that particular point you might have some voltage on this particular line you might have some particular voltage you might have some particular voltage on that particular line do you see that everyone everybody is able to see this clearly okay so how much is that field and how much is that voltage comes via derivation where you have to find the field due to this field due to this add them vectorially and you get the field similarly potential due to this potential due to this add them and you get the total potential so that derivation not so important but main thing is what is the value that you get so for doing that let me just extend this line first let me just extend this line first the field is making some angle Alpha with this yellow dotted line and this yellow dotted line is making some angle with the dipole moment let's say I call it Theta let's say I call it Theta with the dipole moment the position how far I am how far I am is making some angle and this is some distance so this field and this potential is given as follows this electric field is given by kums constant your dipole moment divided by R Cube R is this R is this I'll just repeat over here here you have your dipole moment and you here you have your R Cube and here inside you have root of 3 cos² thet + 1 3 cos² Theta + 1 this is the formula for finding the electric field at some distance r at some distance R this is the formula KP by R Cub < tk3 cos² Theta + 1 what an interesting formula and this angle which the field makes with the position Vector can also be written down so that tan of alpha is actually is actually the tan of theta divided 2 it is not tan of theta by 2 it is the whole tan thetas by 2 be very very careful so tan Alpha is tan Theta by 2 that is the other formula which you must know the last one is of the electric potential the electric potential at any point is given by KP p is that electric dipole moment divide divided by this time R square not R Cube R square that's it and you put over here COS of theta you put over here cos Theta COS of theta that is the value of the potential at that particular point that is the value of the potential at that particular Point very very important I hope after this you understand what it actually means to find the potential and find the field at any given location this is the field and the potential diagram you actually finding the field and the potential at this point by substituting these values now another important thing another important thing over here is there are some special locations in this entire diagram which I will show it to you I'll just create a duplicates go down over here and there are these special locations in this entire thing one over here is basically this particular position called as as the a axis of the dipole this is this is basically also called as the axis of the dipole let me just show it to you over here this is the axis of the dipole so anywhere on this line it is called axial position this line over here which is exactly perpendicular to it which is exactly perpendicular to it that is basically called as the equatorial position this this particular line that you see this is also called as the equatorial position or equator of that dipole which is exactly perpendicular so let me just show it to you over here this is the Equator this is the equator okay now if I use that formulas and find out what is the field on the axis versus field on the equator Etc the field on the axis field on the axis if I use this formula where is this yeah on the axis what is the speciality this point will come here the Theta will become zero the Theta the Theta on the axis will definitely become 0 degree everybody agrees so just substitute zero over here just substitute zero over here in fact you can also become 180 if you are on this side then imagine if you on this side then the Theta value will become 180 that is also okay so 0° or 180° either ways when you square the cos because COS of 0 or COS of 180 both is 1 minus one squaring it will make it 1 1 into 3 3 3 + 1 4 root of 4 is 2 root of 4 is 2 so hence it will become 2 * KP divided by the distance let's say it is R Cub that is what the field on the axis will be that is what the field on the axis will be if you go on the equator if you go on the equator and think about it if you're on the equator then this angle will become 90° or minus 90 that's okay so at the Equator the angle Theta will become plus or minus 90° so the electric field on the equator will become just check this out put cos 90 cos 90 is 0 0 into 3 0 0 + 1 1un 1 1 so KP by R CU so it will just become k p by R Cub that means the field on the axis is BAS basically two times the field on the equator is two times the field on the Equator so the field on the axis is two times the field on the equator that's a very interesting relation that you get here the field is strong makes sense because the lines are closer here if you see the lines are far away that's why the field is weak so that number two is missing here that number two has come because lines are closer so the closeness decides how strong that field is going to be hello ad is that clear everyone if you talk about the voltage I already mentioned voltage on the equator will be zero voltage on the equator potential on the equator will always be zero okay it will always be zero you can see that right so this is very very important direct formula based questions come on it I mean there is nothing great other than that okay so uh I think we have done this properly so don't need this okay all these formulas also I kept here by the way uh you don't need this if I have this okay one thing that you should keep in mind all these formulas whatever I have written over here right these are only applicable under a special condition that condition you be careful that condition is only if you are really really far away from the dipole basically your dipole length is much smaller as compared to where you are it cannot be very close by you have to be really far or if you are somewhere the dipole length is short the dipole length is short that means it's a short dipole so this is the short dipole so the dipole is basically short as compared to where you are only then these formulas are applicable or or else it's going to be just like finding any other normal field or potential you find the field due to one charge due to other charge do the vector addition find the resultant just like how you have been doing before so then it is a standard thing okay these formulas are only applicable for short dipoles right so let's see if you guys can solve this particular question coming up on your screen the distance of the field point on the axis of a small dipole is doubled by what factor will the field due to the DI dipole change interesting think about it and answer think about it and answer come on my dear students what do you think will happen the distance of the field point on the axis of a small dipole is doubled by what factor will the electric field due to the dipole change in general what is the electric field formula it is basically KP root something divided R Cube so the electric field is inversely proportional to R Cube so think about it if the distance is doubled if you make it two times the denominator will become the denominator will become eight times so the electric field will become 1/8 of the previous value yes by what factor 1/8 if it was eight it will become one if it was 16 it will become two it will become eight times of the 1 by8 times of the previous one so that is the answer is that clear my dear students is that clear my dear students yep everyone all right all right one interesting question which I had found uh for electric field and potential was this one I think okay wait I'll just put it over here uh this was interesting question which I had seen where there is one dipole here and another dipole here p and p okay and you are considering a point over here uh which is having the coordinates a comma 0 the question is find the field over here and also find the potential at this point it's a very interesting and nice question on the concept of uh you know the fields and the potential due to Electric dipole okay so basically it is just using these formulas properly so let's try to see how do we solve this particular question so first of all let's go with the potential first because I feel that is the easier part of the two then we can go to the field part then we can go to the field part okay potential is much easier observe this carefully now let me split these dipoles into two parts one dipole horizontal other dipole vertical for the horizontal dipole this point are you on the Axis or are you on the equator are you on the Axis or are you on the equator thank you J preparation so much my God thank you so much for the Super Chat you deserve an appreciation where is it our life class let me show this to all of you even those who are watching it later on yes thank you J preparation so much for that humble contribution of 40 books thank you thank you so much means a lot it shows your immense love and support So guys if students are doing so much for us you definitely should smash this like button right away right now subscribe to the channel and not just subscribe okay you should also hit all you should also hit all okay so make sure you subscribed make sure you liking this video yes make sure you're doing that thank you so much guys thank you so much means a lot these small gestures truly okay now because of this blue drole you are on the axis okay so at this point as you are on the axis as you are on the axis the dipole contribution in the potential will be KP cos 0 remember because you are on the axis Theta will be 0° divided by distance which is basically a square okay so it will become KP by a square KP by a square because of this dipole you are on the equator isn't it for this particular dipole just think about it what is this position it is a equatorial position so the potential on the equator is always a big fat zero that is something what I have been telling you here also where is it potential on the equator is zero if you are not on the equator just use this formula which I have been giving you where is that KP cos Theta by r² already given perfect so hence if I ask you what is the total potential what is the total potential because of both the dipoles add this with this it will just be KP by a s+ 0 which is just KP by a square that's it that is the answer of the total voltage at that particular Point yes or no everyone with me everyone with me clear excellent day now that this this is understood let's go to the more tougher part yeah I'll tell you why it is the tougher part because a lot of students make some stupid mistakes here and that is why we should discuss this problem imagine for this horizontal dipole you are again on the axis this point is on the axis so on the axis the electric field on the axis the electric field is k p but two times remember 2 * k p by distance Cub perfect if you consider this particular dipole you are on the Equator so the electric field on the equator is just KP / a CU so like okay let me add them but be very careful electric field is a vector it's not like simple potential where you just add them just with a plus minus sign no you can't do that it's a vector potential was a scalar so that is the catch that is the catch did you get get it so how do you resolve the catch okay I can't just add them directly I need to see the directions on the axis notice coming back coming back over here when you are on the axis the electric field lines are along the dipole moment check this out electric field is along the dipole moment when you are on the equator check this out the electric fields are opposite to the dipole moment yes or no on the equation electric field lines are opposite to the dipole moment very very important and interesting thing you can see that the electric field is basically anti- parallel is anti parallel over here whereas over here the electric field on the axis is parallel to the dipole moment so that is the thing which you need to keep in mind which you saw from there coming back over here so for the actual part for the actual part the electric field will be like this electric field for the actual part for the equatorial part it will be anti-parallel that means it will be opposite to this dipole moment so this is e equatorial now we know where the net field will be now we know where the net field will be it will be in this direction this is the net electric field and since both of them were perpendicular to each other so this electric field will be electric field along the axis square plus electric field along the equatorial Square Pythagoras both are not same but some terms are common like KP by a CU so I'll have root of 2 sare + 1 square 2 square 4 4 + 1 5 so it will become KP < TK 5 by a cub that is the net electric field what an interesting question what an interesting question Perfecto always thank you yat clear everybody with me right amazing right so this is a very good problem where that confusion of electric electric Fields Direction happens and when to use which formula happens and the best part is in the electric field where the electric field is only in a different direction all right so this is a proper I would say level three question as a proper level three question so I hope you enjoyed this question let's go to the final part where you have dipole in an external field where you have dipole in an external field okay so we just now studied that an electric dipole basically an electric dipole basically creates its own field and potential but what happens when you put this dipole in somebody else's field in somebody else's field that is the last Concept in this particular chapter by the way let me tell you I'm following etyma flow I'm following Hyma flow so whatever is there in Hyma very very similar gal take 90% 90% of the flow I'm maintaining through HMA book okay so yes let's see now imagine I have an dipole this is positive this is negative and maybe I have some okay okay I have some electric field going like this like this this is some electric field this is 100% non-uniform non-uniform And if you notice on the negative charge this electric field will apply a force maybe this is f negative on this it will apply a force like this F positive why this way because on the positive charge the field and the force are parallel on the negative charge the force and the field are opposite that's why like this these forces are in weird directions like you can see so if I try to find the net force which is f+ f minus 100% it is not zero not just that if I try to find the torque on the dipole the torque on the dipole obviously these forces are not collinear remember only when only when you have Co linear forces colinear forces the torque is zero but the moment the forces are like this or one of the forces like this and the other is like this then the torque is not zero right so these forces are definitely not colinear uh you can see that definitely the torque on it is not zero the torque on it is not zero so there is some torque which is going to act on it and it will try to rotate it 100% so if you have a non-uniform field depending on case to case there might be Force there might not be Force you know there might be torque there might not be torque but main thing is net force is not zero torque being there not there that's secondary but Force well that is different that is different direction different magnitude also so net force is not zero in a non-uniform field but the moment I switch over to a uniform field things change see this is uniform field what is the speciality of this the speciality of this is this is uniform uniform field of somebody else because the field is uniform what you will see is that the force on the positive charge versus the force on the negative charge both are equal and opposite because the field here field here is same force on positive in the direction force on negative opposite the direction equal and opposite so if one were to calculate the net force on it the answer will be a big fact zero so the net force on a dipole on a dipole in uniform field in a uniform field is always zero this is very very important is always zero but in a non-uniform field you can see there are cases where it may not be zero but here it is always zero in uniform field and that to the net force this is very very important now you might be wondering is there any torque acting on it the answer is well there is torque in this situation because the forces are not along the same line they're separated by some distance but if the orientation was slightly different maybe there would be no torque so if you talk about the torque the torque May or may not be zero may or may not be zero because it depends on the orientation it depends on orientation of that particular dipole let me explain how imagine the dipole was like this versus like this versus like this and the external electric field which is there it is like this is like this and like this if you notice over here the force on the positive is like this force on the negative is like this here force on the positive is like this force on the negative is like this force on negative is this way force on positive is this way in this particular problem I hope you see that because of these two forces there is definitely a to this way in this problem forces are colinear so the torque is a big fat zero in this problem these two forces will tilt the dipole in this particular manner so there is torque in clockwise Direction so clearly the torque depends on the orientation so it may or may not be zero is this point clear is this point absolutely clear my dear students now if I ask you how much is the torque well that's not a big task to find see this is the dipole this is a dipole of certain length and there is plus Q charge and minus Q charge over here and you have a force over here and you also have the force over here to find the torque right the general formula for torque of a couple this is also like a couple Force this is like a couple Force by the way because forces are equal and opposite so for a couple Force the torque that you will find the torque the torque that you will find is always any one of the one of the couple Force One of the couple Force multiplied by multiplied by the perpendicular distance between the forces meaning if I drop a perpendicular distance between the forces multiplied by the perpendicular distance between the forces to multiply it you get the torque you will get the torque that's it as simple as that so here the torque will be any one of the force is basically F in the later on stage I will write it as Q into e the perpendicular distance well let's say this is Theta so this this is L so this is L sin Theta so this is L sin Theta now you can see charge and length can be combined together and written down as p and electric field let me just keep it as it is this is your electric field the one over here so as it is and sin Theta also I'll leave it as it is p is sin Theta so that is basically your torque that is basically your torque now the best part is p is a vector e is a vector yes p is a vector e is a vector electric field electric field is also a vector electric field is in this direction and Theta sin Theta wow this is a vector product 100% Vector into Vector into sin Theta vector vector product so guys I can write this as torque Vector is the electrical dipole moment cross the electric field cross the electric field so this is a very very important relationship of the torque acting on the dipole P cross e p is sin Theta wow luxury Hitler my 2024 bad student where are you these days counseling process is going to begin madum rames I'm expecting it to be completed in August September that is the Target because we are going in full swing if you notice like two two chapters per week if you just I mean even think about it per subject that's around roughly five to six chapters per week we are trying to complete so not much time August September September we are targeting yeah we should be done by that okay yes same energy because uh for every student coming every year I am the same right I mean it has to be the same you can't say that I had a lot of energy in 2020 now in 2023 less energy 2024 even lower energy not possible so you need to have that same energy in fact it is getting better I feel with lot of colorful diagrams okay I use little bit lesser colors initially now I'm using even more color looks like a coding right python C++ your syntaxes it's looking like that okay yeah hopefully you will get into n don't worry so this is the torque acting on that dipole now the uh interesting part about this whole thing is when I show it in different different arrangements and the feeling that I will get see what do I mean by that imagine I keep the dipole oops imagine I keep the dipole exactly opposite then I slowly turn it like this then I make it like this then I will make it like this then I will make it like this then I will keep it like this then I I'll will keep it like this then I'll will keep it like this just showing you some orientations of the dipole versus the electric field versus the electric field okay electric field is always here electric field is always here like this okay so assume green is always the electric field the pink one is always the dipole moment everywhere now in each case can you think what is the torque Direction if at all in every single case I feel see p is here e is here P cross e so the torque will be like this so the torque will be like this right here if you notice p is here e is here so the torque will be in this direction here this direction here this direction here oh zero they are parallel so the torque will be zero no torque at all here it will be like this uh here again it it will be zero because they are anti parallel sin 180 is zero here it will be like this here also it will be like this looking at all these diagrams you know what sense I'm getting what sense I'm getting look at two special positions in this entire diagram there are two very unique things in this entire diagram one is this one one is this one and the other one is over here the other one is over here just imagine the dipole was perfectly aligned with the field perfectly if I move it slightly on the top the torque pulls it back if I move it slightly below the torque pulls it back in fact if I make it perpendicular like the one here it still pulls it back over here if I make it perpendicular down it pulls it back if I move it too much Behind still it tries to come back if I move it the other way too much back it again tries to bring it back here so it's always trying to come back over here so is it not a position of stable equilibrium I mean obviously it is an equilibrium because stock is zero but it is not any ordinary equilibrium you try to dis disturb it it comes back you disturb it it comes back some people are there like that they are so focused on J and I observed this even when I interviewed The Toppers so many of them you know it is very simple to talk to them it's so straightforward with them that I asked them uh were there any distractions no I asked them did your friends try to distract you well not so much but few friends tried to tell me to watch this watch that uh I said no I have to watch J uh lectures or would you like to play outside for this thing let's go party no I have to study uh school well not so important boards is not so important I have to prepare for J it's so straightforward like so stable you try to deviate them they'll come back you try to push them here they'll try to come back so it's very simple guys to become a 99.9 percentile student or to top in J so this is exactly that kind of a thing so hence I would say this is a stable equilibrium position stable equilbrium position do you agree with me whereas just look at this this is that H low percentile I mean in equilibrium lecture is going on equilibrium lecture is going on you move it slightly here goes to the other side you move it slightly down like the one shown here slightly down Z it goes to the other side so the dipole over there in that opposite orientation was in equilibrium but a small disturbance here or here Z it takes it far away from that so it is highly unstable it's highly unstable so this is unstable unstable equilibrium do you guys agree with me on this do you understand the difference between the two yep yep very good very good yes just like me very focused came to the J lecture even after this exam happens you get so engrossed in the exam and then finally you will somehow achieve a lot of concentration even after the exam crazy it is okay so this was 0 de angle this was 180° angle till this point I hope everything is clear by the way if I ask you when is the torque maximum if I ask you when is the torque maximum well it is at 90° and you can see it very well uh you know over here you can see that this is the scenario of Max torque Max torque which is at 90° plus or minus this is also maximum torque this is also maximum torque again this is happening at perpendicular okay so torque is maximum at 90° great so you have seen how the torque changes how the equilibrium positions are how forces are zero and how the force may not be zero if it is a non-uniform field is one last thing over here and that last thing is basically the energy how many of you feel that looking at this diagram it feels like a spring it feels like a spring which is like you know it's stable here in this position if you try to move it here it comes back you try to move it here it comes back you try to move it here it again tries to come back you try to move it here it again tries to come back so it's like your spring is being storing some energy and it's bringing it back over here it feels like that so this is going to have some kind of electrical potential energy and we Define that energy to be zero when the dipole is perpendicular to the electric field it's just a convention don't ask why but it is a convention that a dipole when perpendicular that scenario that particular particular scenario of 90° is taken as zero reference potential this is your zero reference potential energy zero reference potential energy so there is electrical potential energy involved as well over here and you will see that you can find that again using integration it's not that difficult the main thing is the formula over here the electrical potential energy comes out to be minus minus P minus p and into e minus P into e and then if let's say for example this is your dipole and uh this is your electric field and the angle between them is Theta so what comes out is minus P cos Theta p is a vector e is a vector energy is a scalar and there is cosine obviously there must be a product over here so the actual formula turns out to be U is equal to Nega negative P Vector dot producted with DOT producted with electric field Vector so this is what the electrical potential energy formula looks like this is what the electrical potential energy formula looks like very very important all right okay I hope this is absolutely clear awesomeness awesomeness great Okay cool so with this if I go back over here and if I ask you what is the electrical potential energy in this situation of unstable equilibrium the answer will be check this out minus p e cos 180 because Theta will be 180 cos 180 is min-1 -1 into -1 + one so it will become plus P so it will become plus P if you ask me what is the potential energy here in this scenario so you'll be like okay let me just figure it out Theta is 0° substitute 0 cos 0 is 1 so it will become minus P so it'll it will just become it will just become minus PE interesting thing is this is the minimum potential energy which you can have and this is the maximum potential energy which you can have it kind of makes sense because when you are unstable your energy will be very high unstable too much energy hyper like Madness you have energy so maximum energy at unstable and least energy in fact negative energy in the stable equilibrium position that is what it is very nice cool so maybe we can solve a question on this what do we have positive charge is fixed at the origin of the coordinates and electric dipole which is free to move and rotate is placed on the positive xaxis its moment is directed away from the origin the dipole will what will it do draw the diagram it's a non-uniform field question it's a non-uniform field question think about it it's a nonuniform electric field question how because look at it a positive charge is fixed at the origin so you have a positive charge which is fixed at the origin this is your x-axis this is your y- axis an electric di which is free to move and rotate is placed on the positive x-axis free to move such that the moment is directed away from the origin so this is how you have plac the electric dipole moment now interesting thing to note is how the uh electric field Lin will come out of this how the electric field lines will come out of this electric field lines will be like this then like this like this notice this is how the electric field lines will come out of this 100% these electric field lines are non-uniform in fact the field is very strong here and it is very very weak as you go far away so which means when you calculate the force on the negative charge on the negative charge the force will be higher versus on the positive charge the force will be smaller these both won't be equal F negative magnitude wise will be more than F positive so hence the net force on it hence the net force on it will be there towards the hence the net force on it will be there towards the origin so what will it do it will move towards the origin that is the answer it will be the answer there will be no torque on it because both the forces are coine the net torque will be zero since the forces are cinear forces are Co linear forces so they cannot produce any torque only when you do this there is a torque when the forces are along the same line how will there be a torque there must be some separation okay there must be some separation so that separation is absent so hence there is no torque but there is net force towards the origin is that interesting everyone clear okay all right all right perfect moving on to the next question what do we have two charges level two question of magnitude are separated by4 mm makes a dipole the dipole is placed in a uniform field of 10 dine per cent per Kum sorry per Kum making 30° with E the magnitude of the torque is how much field is given in dimes per Kum angle is given distance is given charge is given finding the torque well well well torque is p e sin Theta dipole moment is charge into length so charge into length into field into s of 30° so I think now you just have to substitute every single value the charge is 01 so instead of Q you will put 01 length4 mm so4 into 10 the power -3 into the field 10 dmes well 1 Newton is 10 the^ 5 dimes 1 D is 10^ minus 5 Newtons so 10 into 10^ - 5 Newtons and Kum as as it is sin 30 is just half come on four is there two is there so answer will be two into something so check the answer it is D I didn't even calculate I didn't even calculate this I mean I just saw only one number is there here and here so I know the answer will be 2 into 10 the^ something and that something doesn't matter for me because there is only one option with the number two so directly I will mark it as option number D but I know if I calculate this I will get it as 10 the^ minus 10 this is called as the ignoring powers of 10 zeros and decimal places if you have been staying with me for a long time uh you already know this trick and technique which we have been using for calculation purposes right very simple because the decimal places don't matter the powers of 10 don't matter the zeros don't matter numerical value will be 4X two 4 by two which is two is only there in one option if two was there in two options or three options then there was no other choice but to solve the comp complete powers of 10 that is a trick for it okay well that is the lecture we have completed this chapter part one part two basically goss's law is a separate chapter in heta and many books obviously if you are using coaching material also many times it is separately printed so we'll be doing it on Tuesday if I'm not wrong or worst case Friday and till then please revise this chapter properly solve the questions solve the dpps The Jungle Book will contain the DPP of every single chapter check it out the link of the Jungle Book is there in the description box basically Jungle Book is a single resource sheet for all the subjects all the lectures no playlist required anymore you will get all the lectures arranged in the sheet the notes will be arranged in the sheet the dpps will be arranged in the sheet so everything in one single place my dear students okay so that's why we call it as a jungle book and our series is lion come on Roar series so that's why we have the jungle theme so if you loved this lecture I want every single student of 12th standard put up in the comments 12th standard started everybody in the comments 12th 12th started 12th started with full Joy sh with heart with a smiley whatever you want to put but everybody is going to comment this okay thank you so much guys thank you and if you not had dinner please have it okay we'll be meeting very soon bye-bye Captain sh signing off Asa