Transcript for:
Understanding Electric Charges and Fields

hello that is 12th standard chapter in physics so physics electric charges and Fields so two and half to hours minimum are you ready to stay with me till the very end so ex I'm not going to teach you anything extra so high Lev so problem teaching session I will it on a separate day are you all okay so that is a plan so okay this is for 12 standard electric charges and Fields chapter in part one physics that will be a huge motivation for us teachers okay and if you already subscribe to the channel then smash the like button I know that very well I will try to do justice to 12 standard I'm I'm taking a lot of effort for you guys in the sessions I'm trying to cover everything so please use this properly and let's all grow together okay great so elect charge okay elects you get two words elect so please everybody I want you to be patient in the session so I will cover everything the session you will thank me later okay I want to tell that in the beginning itself now let's get started meaning charge Statics static at rest so if you say something is static that means it's at rest so so elect it deals with the study of force fields and potential rising from static charges so static charges now the charges which are not moving the charges which are not moving so n charges electrostatics so now let's move forward so elatic how many of you have experienced electrostatics in your own life have you guys have you guys own have you guys experienced it sta electricity okay so experience AR aren't you guys aware of that very good super super so if you have bits of papers if you have bits of papers if you I'm sure all of you have experienced that so examples of electrostatics so that is basically charging scale bits of Pap okay so people notice that there are certain pairs of object which start attracting each other once they have been rubbed together example glass rod and silk so glass rod silk clo both will get charged so they will start attracting so this attraction was not happening before the objects were rubbed together so rubbing they are getting charged so this is one way of inducing charge hello you learning something here one way of charging is by friction So when you say rubbing it is basically friction so when you have friction you can charge your objects correct so ways of charging by conduction by touching by contact okay great El okay so that is the history behind got it so objects exhibit glass rod plastic and fur so plastic animalur you will get charge so the rod usually takesi no people don't know so glass rod becomes positive silk becomes negative plastic rod fur animal fur plastic rod will become positive animal fur will become negative so please not it down want to cover everything I hope all of you are happy now let's move forward these observations were beginning of Science of electricity so they were surprised we know the reason and we are all very casual when they experienced it first they wanted to know what is the science behind so this was the birth point of electricity studies the study of electricity or study of charges okay and example tap water rer and the tap water will get attracted again because of charges okay great super pangla let's go forward so researchers believe that rubbing objects with one another gives them an invisible property that enables them to attract each other okay so charging Bas so Benjamin Franklin gave this property the name of charge so rep what is the property that makes them attract that makes them repel so charge so Benjamin Franklin okay and later researchers were able to confirm there are only two types of charges one is positive charge is negative chares later on they were able to find out positive negative chares because of electrons THS JJ Thomson experiment important I'm sure all of you are aware of it so JJ thompsoni charges were also the other kind got it great so POS Sil becomes positive and the silk becomes are you all clear sir plastic rod plastic rod negative sir you read NCR NC I'm having the entire textbook here NC textbook I have referred everything and made the slides so read your ncrt carefully okay the plastic plastic rod glass rod please check it out if I'm wrong I'll correct it right now itself okay so plastic rod will will will be rubbed with cats fur repelled each other okay on the other hand plastic rod attracts the glass rod okay plastic rod positive posi negative I will correct myself please write it down again okay so please write it down glass rod it is positively charged and silk it is negatively charged plastic rod again it is negative glass rod plastic rod they will attract each other okay great great so that is from your ncrt you guys can check it on page number two how many of you how many of you have understood that unless you read that information so please note this down please note this down in mcqs they can ask you they can ask you especially those who are studying for neat or J mains you guys should be aware of this that is very very important great great great so can anybody tell me what is the sign of what is the sign of f the sign of f is going to be positive so glass rod will repel the fur glass rod will attract plastic rod plastic rod and silk will repel so this is just basic information so for negative please not it down that's wrong this is only correct what I written it here is correct and of course it's information so basically you have to remember it okay so you are number two types of charges so Franklin chose negative for one type and positive for the other type got it and positive is for the glass rod and negative is for the silk and JJ Thompson found out electron electron not negative charge negative charge number silk cloth glass rod is positive I hope you're all clear everybody okay so now what is the unit of charge the unit of charge is nothing but your kulum okay and a Kum is a very big unit I hope all of you are aware of that Kum is quite a large unit for all practical purposes but still the SI unit of charge is Kum so Kum is very important please note it down so positive charge and negative charge Ty and chares because of flow of electrons because of transfer of electrons so electron charge electr it is 1.6 into 10^9 okay it is + 1.6 into 10^ minus 19s so I want you all to be aware of that so how many electrons do you need for one of charge frequently Asked question so please refer to it correctly and tell the answer are you all ready shall I move forward Palani super P so 6.24 into 10 the^ 18 6.25 into 10^ 18 absolutely correct fantastic let me write that as well so 1.6 10^9 so it is direct variation so direct varation you do it like 1 into 1 by 1.6 into 10^ minus 19 so electr you will get 6.25 10^ 18 electr one did you all like it are you all happy so electr one of charge has flown okay one of charge has flown are you all clear very good can a neutral charge get attracted by negative charge neutral charges cannot be attracted but when you bring a negative charge near a neutral charge you can induce charge mishwar so the induc charge it will induce one one type of charge another type like that you can create charges I will come to that please wait a minute okay so shall I move forward Square where is the energy I want everybody to be respons in the chat I want you all to be very very agile very very responsive in the chat sir slides kuring sir yes I will share the slides after the chapter is over I will create a separate web page for it to share the slides okay super level are you all happy superb so now let's go forward so properties of electric charge electri please note it down either Bas P questions they can ask you in section b or section c or section D what are the properties of electric charge so please remember all of them so we have adity of charges adity of charges so if you have a if you have a isolated body and you have charges let's say one I can say the total charge of this body is what I can say the total charge of this body the total charge of this body is equal to plus two because charges can be added so of charges so total charge Express so in the property of charges wherein they can be added and you can find a net value of the total charge additivity of charges are you all clear very good so R is a very important thing R is a very very important thing okay so quantization of charges quantization of charges it always be multiples of electric electron charge okay our our charges it will be a integral multiple of electron charge you find in this world it will always be made up of integral n on the inte integral number of electron charge integers now it can be + one uh +2 + three + 4 and my up to Infinity it can be zero it can be minus one it can be minus two it can be all the way up to minus infinity are you all clear everybody happy so electron charge integral are you all clear everybody happy super very good very good so and the so for example our body is made up of cells number of cells will be an integer object will be integral number of electron charge this is what we call as quantization of charges okay conservation of charge isolated body charge can neither be created nor be destroyed so conservation of charges the total charge of an isolated body will never change it will be the same okay so because why do we say this because charges can neither be created nor be destroyed okay are you all happy so very good very good so what is q q charge symbol okay great question super soang additivity of charges the total charge of the system is obtained by adding all all the charges algebraically algeb with the sign algebric with the sign so plus minus total charge of the system so adity of charges I hope all of you are able to understand okay so charge has magnitude but no Direction just like Mass so charge magnitude Char okay great so now this is quantization of charge it is made up of integer number of electron charge integers 1 2 3 4 5 -1- 2- 3- are you all clear everybody happy superb you guys are awesome I coming in order participation invol okay are you all clear very good so so charge must be a multiple of charge sir charge on any body should be a multiple of electron charge so charge is not a multiple of charge charge is a multiple of electron charge so charge on any body should be an integral multiple of electron charge so so in the body we have minus five 5 e charge plus three charge plus 2.0 charge minus 1.5 e charge so so in the body minus 5 charge in the body plus 3 charge in the body plus 2.0 e charge okay and in the body you have minus 1.5 e charge so can you all please let me know sir 1.55 very good that's right you are correct so that is what I wanted to convey I wanted to convey that right because minus 1.5 fundamental building blocks of charge is electron charge so any multiple of e is fine but electron so that is why this is wrong are you all clear but 2.0. sir how is Sir negative Char of course not you have positive charge also minus5 into e so minus5 into eus 5 into elect charge so that will be a positive charge I hope all of you are clear are you all happy with that so positive charges we have to make n as negative e it's a negative number electron charge electron charge- 1.6 into 10us 19 so n posi whole charge will be negative negative whole charge will be positive okay are you all clear fantastic you guys are absolutely amazing keep it up let's go to the next concept right now so conservation of charges for an isolated system isolated system now away from all influence system system charge can neither be created nor be destroyed so net charge of the isolated system will always remain constant charging by touching okay so let's say you have a negative charge Q you all know that Char by touching charging by touching the charges will get distributed in such a way that they'll have equal charges the steady equilibrium state so charging by touch I hope all of you are able to understand so the negative Char some of the negative charges will flow in okay it will develop charge q by2 and this also deop wait so it is called touching this is by contact okay this is charging by contact I hope all of you are clear charging by contact St there'll be no more transfer of charges so State they'll have movement of charges charging by touching please remember this don't forget it okay now what are conductors what insulators whatever allows the flow of charges whatever allows the flow of electricity through them so those are called as conductors so conductors speciality they will have free electrons they will have mobile Char charge carriers mobile free to move okay so conductors special they will have mobile charge carriers they allow free electrons that can carry the flow of charges so so conductors are able to support the flow of electrons I hope you understand insulators free mobile charge carriers ins they do not transfer current they do not let the flow of charges okay so insulators are those substances which do not allow the flow of current conductors are those substances those materials which allow the flow of current what is the best conductor silver gold copper they're all very good conductors what is a bad conductor you have so many examples of bad conductors you have okay is a cond wires of wires work okay so now let's move forward Pang insulators are materials that do not allow the flow of charges through them they lack mobile charged particles mobile now free to move mobile now free to move so insulators they do not have free to move charge particles and conductors you have free to move charge particles that are basically free electrons so free electrons can move and they are the ones which will help in conduction okay so examples of insulators you have glass plastic ceramic rubber wood wool Cork and so on and example of conductors Metals most met Metals conduct electricity silver copper are all very good examples Earth is also a conductor please don't forget that okay semiconductors semiconductors now they have conductivity between your conductors and insulators so semicond cond okay so semiconductors are in between are we going at a good speed are you all enjoying the session are you all happy my dear boys and girls so shall I proceed everybody please let me know quickly quickly very good Frank very good Frank you are right saren fantastic kanishka Gokul hater Great jasica Lost Souls arut selven Santos selven great hash Cham I'm so happy I I don't expect I will ensure that 489 okay great job so now let's go forward sir charging deleted sirp I will quickly run through it I Will Not Waste too much of your time okay so glass if you rub against each other you will have charging you will have friction charging you have taking how do you transfer heat heat transfer conduction convection radiation so conduction when you are in contact conduction when you are in contact conduction so so don't get confused concept so when you have charging by contact charging by touching that's called conduction okay I hope all of you are happy with that and finally you have induction and finally you have induction so so insulators can be charged using friction insulators can be charged using friction so it friction in frictional charging Okay Glass Rod is insulator that is being charged by friction by rubbing against silk cloth okay and the conductors and insulators Condors in contact it will behave as one the charge given to one conductor distributes itself on the outer surface of another okay on the outer surface of the conductor and this distri may or may not be uniform okay soor M it will get split and it will get distributed along the outer surface of the conductor in the distribution may or may not be uniform dep depending upon your conduction depending upon the way you are charging it okay so there are two most common methods of charging a conductor one is conduction and induction so condu please have a look at it so it will give some of the charge here it'll get split so Q now it will become q by2 q by two q by2 q by2 so qge it will get split q by2 q by2 charging by conduction okay are you all happy in charging by conduction both objects get the same type of charge in charging by conduction both the objects get the same type of charge I hope all of you have understood it so please I hope all of you will be ready for that now moving on the next one so induction so induction did you all like it are you all able to understand are you all able to get the grasp of it so induction so induction you have a neutral you have a neutral object thisel positive this posi attract negative andang Still Still this is a neutral body still this entire thing is a neutral body because charges can neither be created nor be destroyed the charge of an isolated system is always conserved so negative negative charge positive Rod will Attract it positive Rod will attract the negative charges nearby and positive charges will go far understood are you all happy so shall I move forward now did you all enjoy it so far so charging by induction I hope all of you are clear now how do you deduct charges on a object so the way you deduct charges on an object on it is by an instrument called Gold Leaf electroscope so so Gold Leaf El it will tell you the magnitude of charge look like this soang you have a glass enclosure you have a r rubber stopper okay you don't want any other influence and you have a rubber stopper and you have a metal rod with a knob you have and you have a metal rod and the metal rod metal leaves thin very thin metal leaves so can you all please let me know you will have conduction will get distributed will each other did you guys like it as simple as that so now it is charging by conduction charging byou so the charge in the Metal Flow in the gold leaves the thin and they will repel each other because light charges repel so they will okay so that is what we call as gold leaf electroscope very important now shall we get started are you all ready session will go on up to 9:00 10:00 so I want all of you to be here until the very end okay and in the chapter you okay so now let's move forward law okay what is the quantity of itch okay so what Kum tried to do was he tried to conduct an experiment where he wanted to understand what is the force between two charged objects which are separated by a distance so let us make a system out of two point charges so1 so now I want to understand so he did experiments so let us say he found out the force between these two is f what is the instrument he used to find out the force between the two charges can anybody check ncrt I want you guys to let me know the instrument he was able to conduct these experiments very good torsion balance very good pya you learned something new so what device he used he used a torsion balance to understand what is the force between these two charges so first set up okay so initial setup ini charge q1 in the side charge Q2 in the side they are separated by a distance of R setup initial setup I hope all of you are clear very good so initial setup he kept one charge q1 here he kept another charge Q2 here and they are separated by a distance of R and on the setup force between them is f is that clear to everybody are you all happy very good very good you guys are fabulous keep it up keep it up so now what he tried to do was he tried to do some experiments so he was trying to not it down what he did so the force comes out to be double of the original Force so charge okay so like that he did lot of experiments beautiful they they have proven things crazy so first experiment he is doubling one of the charges dou four four times origin Force number fource experienced is is directly proportional to the product of the charges M so the force experienced is directly proportional to the product of the charges so Char it is dependent are you all clear so the force is proportional to the product of the charges next he wanted to check he wanted to check what is the dependency on distance next he wanted to check what is the dependency on distance okay so total so they have force between themselves he's trying to understand so he trying to check initial set it be F by distance double Force becomes 1/4 the original value so distance distance double force force becomes the original Force by n so experiment experiment so the force becomes F by 9 it becomes 1 by 9 of the original value so four two square square force is inversely proportional to 1 by r² did you all enjoy it are you all happy so force it is inversely proportional to 1 by r² so force is proportional to q1 Q2 for is inversely proportional to 1 you will get force is proportional to q1 Q2 by r² so in the proportionality remove you will bring in a proportionality constant which is called K so the force is K q1 Q2 by r s kums law Masa did you all enjoy it are you all happy with this my dear boys and girls everybody clear please let me know in the chat very good SVA very good Zolo very good akara great I will do that we will complete do not worry about it fantastic very good so fantastic so okay it is not it is great great you guys are awesome so let's go forward so kums law is K q1 Q2 by r² so number of force electrostatic force is given by K q1 Q2 by r² I will teach you constant so K is nothing but yours constant so value so is 9 into 10^ 9 it is Newton M square perum square radius orance meter and okay are you all happy very good so constant value 9 into 10^ 9 SI units which is your Newton M square perum square are you all clear very good is also equal to 1 by 4ep it is only in space in vacuum vacuum the value 1 by 4 epon in the Epsilon permitivity of free space this Epsilon not is permitivity of free space so so if you keep it in some Medi when we go to the second chapter when we go to electrostatic potential and capacitance there we will talk about dialectric okay so we will see the force value can change so in the set in the set the pertivity will change Epsilon value is only in vacuum is only in space Char I hope all of you are clear very good Superba great great so now epon value please remember that 8.854 into 10 the^ minus 12 units units you can derive it's not a big deal okay so Square per Newton met square epon units okay great so magnitude of magnitude of force okay soii it will be it will be repelling and positive negative it will be attracting R12 r21 don't memorize don't mug up understand I want everybody to understand things and do it okay so shall I move forward great so pangla limitations of kums law no you cannot you cannot apply kums law whenever you want okay so the charges are considered to be point charges the charge Radius 2 m the separation is 3 m so the radius of the charge is comparable to the distance between them you cannot apply kum's law yeahum law is applicable only when the charge is point charge Point charge now the radius should be very small compared to the separation so sear the radius should be very very small so the radius of the charge should be much much lesser much much lesser than the separation between them so it is called Point charge so Point charge Tre are you all clear how many of you are able to understand this how many of you enjoyed this how many of you are able to follow whatever I'm saying are you guys enjoying can you all please let me know in the chat very good Manish I will start chemistry also don't worry about it chemistry is super duper easy very good so let's move forward next liation the charges must be stationary you cannot have moving charges you cannot have accelerating charges so kums applicable when your charges are at rest if your charges stationary it is not moving it will have magnetic field also moving charges can give magnetic field moving moving charges you can have magnetic field created because of that moving charges and magnetism I hope all of you know little bit from the chapter so when you have a charge in motion it can generate magnetic field when you have a charge that is accelerating it can produce electromagnetic waves so when you have a moving charge with a velocity when you have a accelerating charge those cases you cannot apply your kums law it should be stationary only then you can okay are you all clear everybody happy with this super bang so so Vector form ofs law I'm going to teach you Vector form permitivity relative permeability relative permitivity and dialectric constant I will teach you when it comes okay so next chapter is the best place to learn about it please wait for it first let's complete this chapter in the chapter number okay Vector form of law so Vector form of okay so here if you see so if you see this is the origin let's say number first first charge it is at a position Vector of R1 it is position Vector of R2 so Char Vector R1 the force between them is12 by r² R is the distance between them R is the distance between them so distance between them distance between R2 minus R1 Vector R2 minus R1 Vector the vector connecting both of them so R square is nothing but R2 - R1 magnitude Square so please understand the force on Q2 by q1 okay so I will first write that so F21 force on because of okay the force on the second charge because of first one so that will be away from the body because in general we assume that all of them are positive charge in general we assume that all of them are positive charge so12 will we learn that like charges will repel so q1 will repel Q2 correct so I will try to help you out okay very good so the force will be to the right Force value K q1 Q2 by r² R the distance between them the distance between them is magnitude of R2 - 1 R2 - R1 whole Square so Force value Direction r21 sir r21 Direction so r21 cap Direction I hope all of you are able to understand okay are you all happy with this my dear boys and girls so Vector form of kums law so R2 - R1 magnitude you can write as r21 Square okay so that is what they have written here so force on two because of one so let's find out force on one because of two let me see how many of you are telling this correctly for on one because of two because of R charge let's see how many of you are able to answer come on boys and come on girls I want you all to be fast very goodus F21 negative of the other Force very good that's a very smart answer that's a very smart answer but yeah I will derive it for you don't worry so force on one because of two kge charge by the distance between them distance distance between them r it will be to the left I told you by default you have to choose everything as positive by default chares are assumed to be positive so positive positive so the force is minus of r21 so in the r21 is this side so r one opposite side r21 opposite side minus of r21 cap so in the force in the force compare you will get F21 is negative of F12 so the forces are equal and opposite did you all love it was it good s very good I hope all of you are able to follow Pang so top I hope all of you are able to understand if you have any questions feel free to ask okay so force on Q2 because of q1 force on q1 because of Q2 please ask me I will help you q1 and Q2 you have to apply with sign so problem don't up this formula don't memorize this formula the better way to solve is to understand the question and do it that is what I'll teach you I will show you right now okay so deration of the vector form of kums law so now everybody try to solve this Pang I want you all to be fast I want everybody to answer please let me know quickly let me know quickly in the chapter n questions I'm going to conduct previous years questions problem solving so the com S I want all the 12th standard students to be very sincere and serious so please work hard with let me know the chat please let me know and in the session useful micro and micro they are separated by a distance of 20 cm okay they are separated by a distance of 20 cm the ratio of force acting between them will be so force between them now the first charge second charge go so they are asking you what is F12 magnitude by magnitude of F21 we know that F12 is equal to minus F21 so when you take magnitude when you take magnitude both the magnitude will be equal both the magnitude will be equal so this ratio will be equal to 1 is to one you don't even have to one one I hope all of you are able to understand shall I move forward super M Valia 12th will have sessions from from now on every day I will let you know the title in the morning okay great job let's go forward so next topic I'm trying to do it soap In and Out n and Corner we will complete it so that we will do it for chemistry as well okay so now let's get started force due to multiple charges sir I will teach you how to do it it's very simple you have to be good at vectors so Vector resolution how many of you are ready for that 15 20 minutes we will start the dipole deration are you all ready yes great great great super so let's say you have q1 q Q2 Q3 I want to know what is the net force on q1 so you have charge Q2 you have charge q1 you have charge Q3 so you have multiple charges chares so I want to find out the net force on q1 so1 okay so now assume the charges as positive so treat q21 it will be repulsive light charges will repel thece will be like that you guys able to understand are you guys able to catch up yes so repulsive Force the force the so that is a force on first charge because of second charge so fub1 the net force on one is equal to force on first charge because of two vectorially added with the force on first charge because of three so force on first charge because of one it will be along the line joining them but away away because you are relling you ripping means along the line away Q2 and q1 along the line but away did you like the direction are you all happy with it you are getting some clarity over here are you guys able to follow so shall I move forward so please don't add it that is don't add it directly you have to add it vectorially when we solve pyqs when we solve numericals I will teach you CH very good so I hope all of you are clear so formula like I said force on one force on one is equal to force on one because of two plus force on one because of three so Vector force on the charge net force on the charge so F12 now K q1 Q2 by R12 squ R12 already you this is not important this is not even needed okay so let's keep going forward you have n charges q1 Q2 Q3 Q4 Q5 and my q n sir chares what is the net force on q1 net force on q1 so so that is F21 four sorry F12 force on one because of two plus force on one because of three charge Third charge plus force on one because of fourth charge n Force did you all like it are you all happy did you all enjoy it my dear boys and girls yes very good superb Manish kandipa Manish J V level J Valeria superb Vias s very good very good jasica amini fantastic I'm so happy you guys are able to follow so very good I'm so happy you guys have understood it so but examples will take I an I was one of the state topers problem soling I know it's important for a teacher to teach but we will do it but please wait you should have no confusion you should have no secondes great so let's move forward sir K q1 Q3 very good it's K q1 Q3 very good great super I'm glad you guys are following please make that CH okay very good so yeah now let's come back to this topic so we derive certain things we have to Drive the electric field due to a infinitely long wire electric field because of infinitely long plain sheet and then we have electric field due to thin Sher sperical shell okay so we have these three cases to be proven so upo we will use charge densities okay I hope all of you are ready very good super so it is uniformly distributed over cond important okay so shall we get started are you all ready Square energy pangla I want all of you to be very very quick and I want you all to smash the like button in case you are enjoying the video super super brilliant pangla very good what if two forces are perpendicular problem so if you have let's say two forces perpendicular 10 10 Newton like this and 10 Newton like this what is the net force what what is the net force the net force is equal to 10 I cap + 10 J cap so that'll be what root of 10 s + 10 squ so it is 10 < tk2 easy okay it is just 10un it is not difficult I'm telling you again and again problem solving easy so linear charge distribution now when your charge is distributed along a linear object like your wire okay so so let's say Q charge in the linear so charge per unit length linear charge density so linear charge density is nothing but charge per unit length did you all like it so linear object let's say like a wire Char charge if it is uniformly distributed if it is continuously distributed then I can say the linear charge density is Q by L okay are you all clear everybody happy so if I keep it on a Surface sheet 2 surface if I distribute the charge the uni uniform distribute we will we will see area surface area charge density okay so then we'll talk about surface charge density surface charge density is the amount of charge divided by the area of the plane sheet area of the plane sheet are you all able to understand so wire linear object you will see linear charge density which is charge to charge divided by the length of the wire length of the linear object because here we are assuming uniform distribution we are assuming uniform distribution so uniform charge distrib for a linear body like a wire you will take you will take Lambda which is linear charge density for a distribution along a sheet along a PL sheet sheet you will take surface area charge density surface charge density okay you will take surface charge density which is Sigma soite sheet okay I hope all of you remember this and Kia volume let's say you have a spere and the spear and the entire volume of the spear if I distribute charge Q in the entire volume of the spere if I am Distributing charge Qi I will worry about volume charge density Q by V we we usually know by row okay we usually denote by row which is Q by V so Q is the charge the total charge on the spere V is the volume of the spere so volume charge density I hope all of you have enjoyed it so so linear charge density Lambda is Q by L so Kum per meter surface charge density Kum per met Square Q by a q by area q by surface area q is Kum area is me Square Kum per meter square that is surface charge density Sigma then you have then you have your surface charge density I've already explained it then finally you have row row is your volume charge density which is Q by V Q is charge V is volume so the charge on the entire sphere or entire object divided by the volume of the object that will give you the volume charge density okay I hope you liked it you all happy I'm going to use I'm going to use to derive the the electric field for infinitely long wire infinitely long plain sheet and thin sperical shell so I'm going to derive it for you in the class late so in the class in one or two hours are you all with me will you all stay till the very end much Lama much Lama are you ready my dear boys and girls let's complete it okay so yeah let's go forward so electric field everybody listen carefully sham sham sham it's okay we'll continue if I get tired I will take a break but I'm excited so let's complete it okay so this will experience a force corre so thege will experience Force Willi charge posi charge so they will repel each other so we have a force12 by r² Force value so the force will be K q1 Q2 by whatever the distance between them square and it will be a repulsive Force so in the Q experiences a force okay is there nothing over here electri is something which which talks about the influence of Q There is something present which talks about the influence of Q and that is called electric field Masa are you all clear everybody happy so electric field of a Charged particle is the field surrounding the charge particle where it can exert an influence on another charge particle so electric field it is the field around the charge particle where it can exert influence on another charge particle if it is brought here P are you all clear everybody happy super very good you guys are absolutely awesome Q means charge exactly so q that test charge the small q there and the small q test charge Source charge fixed charge okay I hope everybody's a B to follow so properties of electric field electric field is spread throughout the space electric field it is infinite electric field is experienced throughout it will become electric field will become on it is throughout space it is throughout space it is infinite are you all clear everybody happy super the magnitude of electric field can be measured by the effect on charges located in the field okay soest charge Q the electric field is also less [Music] are you all able to understand are you clear very good super pangla so where the force on the test charge is weak the field is also weak the field is also small got it the direction of electric field is the direction of electric force so electri field electric it is the direction of electric force on the positive test charge so the Q sour charge dire if you keep a positive test charge experiencei did you all like it so for positive charge electric field is radially outward but for a negative charge the electric field is radially intive direction of electric field we have to take a positive test charge so test charge posi what is direction of electric field direction of electric field is the same direction as the force experienced by the positive charge by the test charge super so in the test charge Force experiencei negative sir so attractive Force sir so attractive electric field electric field direction is radially inward M did you all love it so for a negative charge the field is radially Inward and for a positive charge the field is radially outward did you all enjoy it so far so good M are you all happy with this my dear boys and girls so shall we proceed neutral charge you don't have field you don't have your charge particles only will have electric field if you have positive or negative charge great great great great so yeah let's go forward so so for a positive charge the field will be radially outward and for a negative charge the field will be radially inward great so what is the electric field what is the formula for electric okay so electric field defition electric field definition the force experienced by the test charge divided by the magnitude of test charge field at any point is equal to the force experienced by the electric charge the test charge the force experienced by the test charge divided by the magnitude of test charge so charge Force experience what is the force experienced if the distance between them is R the force experienced is going to be k q q by r² and it will be radially outward it'll be radially outward so the force is going to be K Source charge test charge by magnitude of test charge r² and direction is radially outward it is radially outward me so it is along along the radius outside so R cap R cap so q q cancel so electric field is just KQ by r² radially outward electric field formula we have derived it I hope you enjoyed it okay so electric field is radially outward for a positive charge and the magnitude is k q by r² so electric field does not depend on test charge it depends on only source charge electri dep everybody happy superb so what is the formula for electric field KQ by r² R cap Direction so what is the unit sir electric field is force divided by charge so force is Newton charge is Kum so Newton perum s unit of electric field Masa are you all happy did you all enjoy it so electric field is force divided by charge so it is going to be Newton divided by Kum are you all happy with this everybody clear shall we proceed my dear boys and girls everybody I want you all to be fast very good very good super Sir W per meter Sol sir yes yes yes electric potential please use whatever I'm showing okay I will teach every chapter one by one I want your support and your involvement that is only thing which I expect great so Electric for because of all these charges is the vector addition of all the individual forces so electric field the net electric field is the vector addition of all the individual electric field super are you all clear so Q electri elect R1 by R1 kq1 by R1 squ R1 cap so K q1 by R1 P now in the distance the distance between them Square Direction so posii will q1 positive charge positive so positive positive it'll be outside so the field because of first charge on P will be radially outward E1 Masa I hope all of you are able to understand so Q2 what is the electric field Q2 so it is going to be K Q2 in Formula electric field formula KQ by r² magnitude so K Q2 by R2 squ Direction R2 cap it is along R2 and out outward it is along R2 radi outward SO2 Direction you have to add it vectorially you have to add it vectorially have E1 E2 E3 e so so you have to add them vectorially you have to do it slowly either you have to resolve it into vectors or you have to use your vector addition formulas which you learned in 11th standard as I teach problem I will teach you all of that don't worry okay so adding them vectorially when you have n charges so then what is the total electric field sir the total electric field is the vector addition of all the individual contribution of electric field super position principle so net force because of n charges net electric field because of end charges is found out by superposition principle which is the vector addition of all the individual contributions super great so I hope you're all clear's nothing inside okay sir in the marathon part one or two hours we will complete it don't worry so yeah please continue to support continue to stay till the very end because we still have many more things to cover are you ready shall we discuss it come on guys don't give give up I want you all to be attentive I want you all to be participating please every single person don't give up guys are you all done with this my dear boys and girls super gamer I hope you guys will participate okay very good so now let's get started exam common so we have one micrum charge and we have two micrum positive so they are placed 10 cm apart at what distance from the one Kum one micrum charge on the line joining the two charges is the electric field zero electric field is mutai okay X do you all agree with me on that are you all comfortable shall I move forward yes are you all happy with it my dear boys and my dear girls everybody cool great super P so uh the field at P because of one one micr charge so k q by r² the field will be to the right side so Oppo is the IAP Direction sir very good plus electric field at P because of 2 micrum k q by r² in a Direction chares so they will repel each other so direction of electric field because of two micrum at P will be to the left sir the minus IAP sir is equal to zero so IAP the minus IAP magnitude should get cancell equal to each other okay are you all clear so mag equal shall we all do that so the magnitude so K into 1 micr by x² is equal to K into 2 micrum by 10 - x squ so k k cancel micr micr cancel so 10 - x by x² isal 2 root root 10 - x X by X is = to < tk2 AO what will you get you will get 10 - x equal to < tk2 x a 10 is equal to < tk2 + 1 into x x is equal to 10 by < tk2 < tk2 + 1 a x is equal to 10 by 1.414 + 1 10 by 2414 10 by 2414 is 4 point something 4 point something answer B so you are right v a level you guys are awesome did you enjoy it was it good how many of you enjoyed it did you all like it are you all happy fantastic very good job jbd oia Babu fantastic you guys are awesome keep it up keep it up so now shall we move forward important so okay so doubt doubt very good has be I will solve pyqs the chap prev questions so very good so go and others who said they didn't follow please revisit this let's go forward electric field lines so sir why are they equal sir PR I will help you don't worry so why are equal electric field at and K into 1 micr by x² I uh plus K into 2 micrum by 10 - x² minus I cap so net electric field at Point P zero so will become mum by x² minus K into 2 micrum by 10 - x² so I is equal to M so left side right so left and right should be equal be I will expect you to know this this much at least you have to simplify great so yeah now let's let's move forward let's go forward is your electric lines of forces okay great so electric lines of forces now it is an imagin con so electric field lines it is just a visual representation of electric field electric field lines or electric lines of forces are you all clear everybody happy super so it is a curve which is drawn in such a way that the tangent to it at any any point will give you the direction of electric field at that point so electric field you will draw electric field lines in such way that this is very important Elric lines of forces use advantage of electric okay so are you all clear so shall I move forward everybody great I hope all of you have understood it is that clear so field lines it is a it is a imaginary thing it is not physically present so it is a visualization thing it is the imaginary thing so they don't have physical implication okay physical existence they don't have so electri please everybody listen carefully so electric field lines they will originate from POS charge so positive charge and negative charge it will come inside it will be radially inwards for negative charge okay so the electric field lines for negative charge will be radially iners and electric field lines for a positive charge will be radially outwards please remember this this is very important okay and electric field lines always represent the net electric field at that point so electric field Lanes cannot intersect each other cannot cross each other exam exam 9% they'll ask you they'll ask you what are the properties of electric field lines Why electric field lines cannot cross each other electric field lines cannot cross each other because Electric how can electric field at one point have two directions that's not possible electric field lines always represent net electric field at a point electric field lines always represent M electric field at that point so M electric field at that point should be One Direction only no how can you have two directions electric field lines cannot cross each other cannot intersect and electric field lines intersect net electric field will have two different directions which is not possible are you all clear Anish I hope you understood very simple concept okay I hope all of you are able to follow so shall we move forward Pang exactly magnetic field lines M yes you are right okay so in the aspect magnetic field lines magnetic field lines they cannot cross each other if they cross each other at the point of intersection at the point of crossing over you will have two different directions tangent to the electric field lines will give you the direction of electric field tangent to the electric field lines will give you the direction of electric field so so I'm getting two different directions I am getting two different directions so this is not possible net electric field electric field Electric lines cannot cross each other are you all clear so electric field lines never intersect each other because at the point of intersection you can draw two tangents at the point of intersection you can draw two tangents different direction that's what I'm telling here so these are all properties of electric field lines so properties of electric field Lin important property they start from positive charge they radi outward from positive charge they come inside to negative charge they are radially inwards for negative charge electric field lines do not intersect do not cross each other okay andang now Electric are you able to understand come me did you all like it are you all clear very good you guys are awesome so now dipole I hope we have covered everything so come on guys let's complete it I hope all of you are with me sir negative charge on electrons negative charge it can be made up of many electrons so that's the difference between electron and negative charge I hope you understood it electric Dio so what is electric dipole let's try to understand that soge positive negative equal magnitude separated by a distance in the setle okay are you all clear everybody happy with that yes we will do it Pam previous question then I will also do neat questions please wait okay thank you Justin that is so kind of you I'm so happy so I will continue to help you guys don't worry okay electric electric electric or positive charge or negative charge separated by a distance okay and both of them should be equal in magnitude so positive charge plus Q negative charge minus Q so magnitude same charge poity poity posi negative so plus Q minus Q separated by a distance set you have negative charge positive charge equ q q so equal magnitude but different polarity negative positive separated by a distance and the separation of distance the distance between the dipole the distance between the charges of the dipole is 2 a this is by convention we follow this we follow this by convention okay y 2A sir which is difficult to difficult to take care of so they have adopted this what is the direction of dipole dipole is a vector it has Direction so the direction of dipole is from negative to positive so the direction of dipole is from negative charge to the positive charge so from left to right is the direction of dipole I hope all of you understood that okay soole magnitude so it is nothing but the charge into separation between them the magnitude of charge separation between them and the direction is along negative to positive so dipole Direction pcap what is P CAP pcap is the unit Vector in the direction of dipole unit Vector in the direction of dipole what is the direction of dipole from the negative charge to the positive charge are you happy very good superb very good AMU am you're right you're right very good super soole electric dipole is defined as the simple product of magnitude of the charge and the separation between them that is the magnitude of dipole what is the direction direction is negative charge to positive charge okay so what is electric dipole it is a vector quantity dipole moment is always from negative to positive what is the SI unit SI unit of uh charge is Kum and separation is meter so the SI unit is Kum meter charge is Kum 2 a separation is meter so that's why the SI unit is Kum meter what is the dimens Dimension is l t a separation is L and our charge I is equal to Q by T current is equal to Q by T So Q is equal to it so I is ampere T is time so ampere time into length l so this is the dimension for dipole electric dipole super did you all did you all like it are you all happy so shall I move forward sir is plus q and minus Q same Mr strange magnitude same polarity polarity positive so poity magnitude same for example plus 2um example minus 3 plus 3um example very good so let's go forward everybody please try to note down this definition especially for how many of you are aware of this yes how many of you have seen this before okay so what is a point dipole when a dipole size approaches zero dipole size now the separation separation is becoming zero and the charges becomes near Infinity then the product tends to be finite such a dipole is called as a point dipole okay so charge is infinity and the separation is almost zero charge is infinity and the separation is almost zero okay set point dipole but please remember the product should be infinity and the form 0 into Infinity form limits and derivatives indeterminate but still you can find out the limit 0 into Infinity is an indeterminate form but still you can find out the limit so the separation is zero whereas the charge tends to Infinity but still the product is finite even though it is zero into Infinity the product is finite such a dipole is called as a point dipole okay so Ro just thein shall we get started yes so ask you dipole or electric field at a axial point and at a equatorial Point okay so in I will give it to you Shimon Joseph at vedantu.com please listen carefully sir so in the dipole line in the dipole Direction the direction now axial Direction so in the direction axal Direction and Bor are you all ready shall we get started very good sir crash sir yes I will make a video about it later in the chap okay very good so a ax along the direction of dipole okay so axial Direction and perpendicular bis sector between the charges equatorial Direction so ask you what is the electric field yes yes GG we are almost done we almost done in know half an hour one hour I will try to complete it okay I'm good I'm good so we will try to complete it are you all ready so are you all happy with that please let me know in the chat okay so I want to derive electric field due to a dipole at a axial line so dipole so in the a in the doubts so let's find out soang in the point p I want the net electric field I want the net electric field at Point P easy question okay I'll teach you why so now the first charge what is the field here I'm trying to find out so Point p l line what is the distance the distance from the center in the center o number Point P distance R okay in the in the distance from Center o is R so the field because of first charge Q at p is what it will be k q by minus a sir how many of you understood that it is Rus a whole square and the direction is how many of you enjoyed it okay I hope all of you are able to follow in the minus IAP I can write do you agree minus I it is from negative to positive so negative to positive now right L Left Right L Left Right L left are you all clear yes Direction minus I ah Q positive charge ahed andus it is a direction of dipole pcap Masa did you enjoy it are you all clear electric field will be attractive yeah electric field you should assume a positive charge here if you have a positive charge at P then minus Q will Attract it so minus Q will Attract it that's why minus Q electric field at P will be towards I so the field because of minus Q will be k q by distance y sir distance R plus a sir R plus a sir so it is going to be r + a whole squ and direction will be direction will be minus P CAP Super A minus P it is opposite to the dipole Direction dipole Direction dipole Direction negative to positive dipole Direction negative to positive so opposite to dipole minus P CAP sir K into minus Q sir don't do that I am taking only magnitude magnitude apply the Direction that's what I will do I will find the magnitude of field you will make m p let's finish it off so dire go KQ by R minus a whole squ minus KQ by r a s Sol you will get 4 a r by r² minus a s the whole Square sir super how many of you are able to do it sir sir r 1 r ² r a whole squ - r - a whole squ by product of these two 2 sir A + B squ minus a minus b square is 4 a sir correct A + B squ minus Aus b square is 4 a divid by r- a into r + a r- a into r + a is r s - a square so I want everybody to let me know in the chat my dear boys and girls please try to be fast I want y all to be quick yes very good super I want you guys to be Crystal Clear practice okaye of dipole the magnitude of dipole is Q 2 a into Q number you will have KP and P 2 * R by r² - a² whole squ super so P into P CAP the P Vector so you'll get k 2 k p Vector R by r sare - A S whole squ answer did you all enjoy it are you all happy ELC field at an axial point so electric aial Point P which is at a distance of R from the center from the middle of the dipole which is at a distance of R from the middle of the dipole this is the electric field 2 k p r by r² - a square whole Square Okay Kevin yes Kevin I am from Chennai I speak Tamil I was born in Chennai man great so I hope all of you are I hope all of you are able to follow so formula they would have told if R is much much greater than a so if p is very very far as compared to the dipole separation if R is very very big so a in the distance half the separation a dipole separ r then r s a s okay let's say R is 100 and a is 0.1 so 100 squ minus 0 r s a s so denominator 2 k p Vector R by r s- a square R sare whole Square so it will be 2 k p Vector R by R power 4 so r r cancel so you have 2 k p by R this is how I want you to solve okay are you all clear shall I move forward great very good we are going to go to question couple I'll go to the next derivation yes sh we will do it sh don't worry so I want everybody to solve it try to be fast try to be quick what is the magnitude of dipole electric field because of the dipole at a distance of 10 cm from the midpoint of the dipole axial line so R is 10 okay okay and 2 a is 1 cm okay and two charges so you have q to be 1 micrum so what is the electric field because of the dipole it is 2 k k is 10 9 into 10^ 9 p p is what p is equal to 2 a 2 a into the charge 2 a into Q so it is going to be 1 by 100 into 10^ minus 6 so 2 KP by RB R cube is 10 by 100b so here you can assume R is greater than a okay sir sir r so take R to be greater than a you solve it you will get I think option C please check it check so you have one Z One Z cancel 2 into 9 18 2 into 9 is 18 answer are you all happy so shall I move forward yes so 10us 10us so 10- 8 10 9 will become 10^ 1 and this will be 1 by 10 whole power 3 so if I come up it'll be 10^ 3 so answer is 18 into 10^ 4 18 into 10^ 4 is 1.8 into 10 power five so option C is the right answer super ah did you all like it are you you all happy so shall I move forward yep M very good so pasang let's go forward to the next question next derivation so in the deration break it through can you all take a break and be back because I want to complete this chapter I I hope at least some of you will come back okay so pangla let's take a break for probably uh or 15 minutes okay so we will continue at 9:45 so we will complete this chapter Pang R easy we will we will finish it so please go take a break and then be back okay dipole in electric field e potion deration then go law then we have to derive derive certain results using law I'll teach okay it'll be it'll be helpful for you okay so 9:45 so I'll go take a 15 minute break and I'll see you guys again bye-bye for hello so shall we get started yes so continue I hope all of you are back electric field because of a at a equatorial portion okay so equatorial portion soole equal and they are separated by a distance 2 Aid question we want to find what is the electric field because of this dipole so electric field because of the dipole now we need to find electric field at P electric field at P because of minus Q charge electric field at P because of plus Q charge so in the r in the r charge are electric field super are you all clear very good are you all happy with thisor pointor point so Point P it is along the equatorial axis okay so along the p and the point P it is at a distance of R it is at a distance of R from the midpoint from the origin so P it is at a distance of R it is at a distance of R are you all clear with that so in the minus the P electri Sirus charge Point P electric field will be attractive it will be towards the minus Q charge don't you all agree how many of you agree with me on that please let me know quickly do you all agree with me on that is that clear very good Aris super minus Q charge positive charge minus Q will attract that so it will be towards that minus Q E minus Q so electric field at Point p is equal to the electric field because of minus Q Plus the electric field because of plus Q electric field because of minus Q electric field because of minus Q will be it will be k q by r² R square it is root of r² + a s squ magnitude of electric field r a a so r a in the it is going to be root of r² + a square Pythagoras Theorem super ah in we should put KQ by r² where R is the distance between the charge and the point the charge and the point so hypotenuse hypot hypotenuse is square root of side squares addition side square square root are you all happy did you all like it my dear boys and girls so magnitude of electric field direction direction from P to minus pus from P to minus Q direction is from P to minus Q next electric field because of plus Q charge so plus Q is positive and electric field at P so positive positive will repel so along the line joining them it will be repulsive so it'll be away from the line joining them so either line joining them the for the the field will be away because both are positive they will repel each other so this is the direction of electric field because of plus Q so what is the magnitude magnitud is k q by r² so again this is R this is a so the distance between them is root of r² + a s whole squ so this is the magnitude of electric field magnitude of electric field direction direction from plus Q to P set did you all like it so far so good so learnly and Q and minus Q electric field form R so Q I only find out magnitude r q magnitude of charge R the distance between the two points distance it is the hypotenuse what is the hypotenuse hypotenuse is root of r squ + a square pus Q so in the in the electric field P to minus Q in the direction and electric field because of plus Q it is plus Q to P it is plus Q Plus Q to P fin I can take care I have confidence very good have answer let us say in the anglea and in Thea it is isoc triangle in the PA a and PB both are equal PA a and PB both are equal it is lying on the equatorial axis so it is symmetric symmetric okay so if it is repelling if it is repelling this place electric field is away in the angle with the horizontal the alternative interior angles are equal alternative interior angles are equal and this electric field is along the line along the line AP along the line AP because it is along AP and outward then this angle is equal to this angle are you all clear so alternate interior angles equal corresponding Ang I hope all of you are clear okay I hope all of you are clear everybody so it properties of parall lines transversal okay are you all clear very good superb yes yes goad yes goad is positive plastic negative okay it is and okay I hope all of you are clear in the in the electric field is along PB along PB along PB now along the transversal along the transversal in the angle equal in alternative interior angles they are equal okay I hope all of you are able to understand are you all happy are you all clear very good VOR resolve vectors resolve are you guys ready so if I resolve the vectors perpendicular hor so perpendicular will be e + Q sin Theta and horizontal will be e+ Q cos Theta correct it's thet techch I'm tol it so it'll become e minus Q cos Theta it'll become e minus Q sin Theta so I hope all of you are able to understand it I hope all of you are able to get it any idea very good super level soe e magnitude so magnitude e eus equ opposite can so the vertical component will get cancelled the vertical component will get cancelled did you all enjoy it was it beautiful so e+ Q sin Theta e minus Q sin Theta canc equal but they are in opposite direction equal but opposite direction right side will get added up so the resultant is going to be 2 e cos Theta direction is going to be minus P direction will take care Direction so because of plus Q E cos Theta because of minus Q so it is 2 e cos Theta did you all enjoy it so 2 e cos Theta is the net electric field at the point p and what is the direction sir direction right side sir the direction of p is minus Q to plus Q negative to positive that dipole Direction so dipole Direction you will get it so e e the magnitude of magnitude of your electric field because of the negative charge or because of the positive charge both are same so 2 e into cos Theta minus answer answer sir cos Theta is base by hyuse so cos Theta is base base is a by hypotenuse is r sare + a s under root so cos Theta so it's going to be 2 k q by r² + a square into root of r s + a square into a in the numerator then minus P CAP that's your answer that is your electric field at an equatorial Point 2 A Q sir 2 AQ is dipole electric dipole value sir so 2 AQ will be electric dipole value so that will be what p and you have K on top of it so P into P CAP will be P Vector so it'll be minus KP Vector minus minus k p into P CAP is p Vector divided by r² + a s power 1 + 1 by 2 power 3x2 so divided by r sare + a sare whole to the^ 3x2 that is your electric field at a point p in the equatorial in the equatorial portion super ah did you all like it was it good are you all happy please go through it I want everybody to let me know quickly AAR very good trishant jagadish etal boy army girl fantastic Shi super shy so deration soial point so aial point we saw it is 2 KP by R Cub Point minus KP by R Cub if R is greater than a if R is much greater than a so this is for axial the electric field at an axial point this is for Equatorial potion so please remember it always are you all clear how to c pic and in the blue you have two e cos Theta you have to add them vectorially soal comp vertical compon I'm trying to add them I hope all of you are able to understand very good super so that's about it so now what happens when you place a dipole in a uniform external electric field so plus q and they are separated by distance 2 a either now external electric field or external electric field I have an external electric field e so what happened I want all of you to let me know so Elric field see the force experienced the force experienced by this positive charge will be e into Q E into q and the force experienced by the negative charge will be e into minus Q so positive charge L of force will be like this and negative charge L of force will be like this do you agree so Rend Force May it'll be equal but opposite in direction right ah it'll be equal but opposite in direction right ah so the net force on the body is zero the net force on the body is zero yeah Force right equal equal because it is uniform electric field net force zero only in equal only in uniform electric field uniform electric field net force zero if you have nonuniform electric field then net force also will not be zero please be careful so uniform electric field please be careful e axial and E equatorial relation sir axial is twice axial is twice your equatorial for the same distance R for the same distance R the magnitude of axial electric field will be double that of your equatorial and the direction is opposite direction for both of them will be opposite okay boss I hope I answered your question Direction opposite and then magnitude of axial is twice that of your equatorial for the given radius given distance okay force zeroi electric field in the plus Q charge will experience a Force Q into e because force in an electric field is charge into electric field so Q into e is the force which is right side because uh charge is positive field is right side and in field is right side charge is negative so the force will be left because charge is negative so net force is zero but torque will not be zero torque will be how much torque is the magnitude of magnitude of the force into separation magnitude of force into separation that is your torque correct Tor magnitude of force into separation I hope all of you are aware of it okay into separation between the lines of forces so Force sir Force Q sir Q the magnitude of force separation separation is when you have an angle th with the with the electric field the separation is 2 a sin Theta sir 2 a I will teach you listen carefully separation distance between the charges plus Q minus Q distance between the charges separation in a dipole okay separation between the lines of forces sear when you want to find out torque it is a separation between the lines of forces soce so separation between the lines of forces line of force on negative charge line of force on posi charge Gap separation between the lines of force okay so it is going to be 2 a sin Theta so is what is perpendicular is perpendicular which we want to find divided by hypotenuse hypotenuse is 2 a so the perpendicular is 2 a sin Theta super so 2 a sin Theta is a separation between the two lines of forces 2 Q 2 a q p 2 a q p e sin Theta so p e sin Theta that is nothing but P cross e so torque is nothing but dipole cross electric field dipole cross external electric field so formula so important so in the what is the direction of torque can anybody tell me so in the example what is the direction of torque can anybody please let me know in the chat quickly so in the ker what is the direction of torque I want everybody to answer try to be fast think about it it is it is into the paper it is into the board sir cross pus Q to plus Q cross e so cross so torque is into the board did you all like it are you all clear so P negative to positive so minus to plus P so P cross e cross I have to curl my fingers so cross e e right so P cross e so into the board is the answer that's what I did Super ah was it good did you all like it what is QE M7 Studios QE is the force experienced by by the charges the force experienced by the charges in external electric field okay Q I hope all of you have understood it so F everybody I want you to be quick come on guys you all can do it I want you all to be fast torque not turning effect you will you will hold at two places you will you will rotate so applying Force I I rotate it like that right so I'm applying torque so torque is turning effect okay so it's a it's a turning effect that you're producing so that is what is torque so torque is basically in rotational mechanics it is it is similar to your force to move a body in a straight line linear motion you need Force you need to give some Force like that for a body in rotation you need torque so torque is similar to force when we deal with rotation got it so answer is C everybody got C okay let's check it magnitude of torque magnitude of torque is what to to is torque torque is equal to uh P cross e so magnitude of torque is equal to P sin Theta that's it so p is what p is nothing but dipole moment is directly given dipole moment is 4 into 10^ minus 9 Kum meter that's the SI unit correct and 30° so sin 30 because it is 30° with the direction of electric field that is what is Theta n Theta is alignment of dipole with the electric field alignment of dipole with the electric field Direction value and what is electric field electric field is 5 into 10^ 4 that's it multiply everything multiply you get the answer so sin 30 is half sin 30 is 1 by two so if you get everything what you will get you'll get 10 power minus 4 so 10 power minus 4 is the answer so it is option C so option C is the correct answer super P rsh very good rsh trishant super trishant you are all absolutely epic keep it up so okay very good so let's talk about electric flux so electric flux it is it is a representation of how many field lines are passing through a given area in a given time are you all able to are you all able to understand so how many field lines are are passing through a area is called as your flux okay so electric field lines pass are the electric flux so if I take an area through this area how many field lines are passing that is going to give me the electric flux okay so it is nothing but it is nothing but your e do a so your electric field dot your area Vector is called as your flux okay are you all clear very good so electric flux and it is the dot product of your electric field and your area Vector area Vector it is always outward normal it is always the outward Normal area Vector it has direction direction it is normal to the surface it is outward normal so pleas is outward normal clear so shall we move forward are you all happy great so e do a what is dot product dot product is magnitude of e magnitude of a into cos Theta so this is your dot product this will give you the total flux okay so the flux passing through that area is found out by this formula are you all clear super p v level Pang siril siril nice to see you yes so now let's move forward I hope all of you are clear number of field lines will change correct the number of field lines passing through it will change if you keep perpendicular then many field lines will pass Ang number of field lines passing through it will reduce correct don't you think so the number of field lines passing through it will reduce it depends on angle it depends on Theta so Theta Z now then you will have passing Theta Z the the area is the area that you are keeping this blue color surface that is perpendicular to your field so maximum maximum is when Theta is one Theta when Theta is zero so when your Theta is zero your area vector and electric field Vector both will be same direction soor electri the very good I hope you liked it great sir difference between torque and couple torque turning effect and couple couple so equal forces in opposite direction SE separated by distance soou couple equal forces opposite direction separated by a distance couple whereas torque is any turning effect torque is basically your R cross F in long okay so torque basically is any turning effect okay any any Force acting at a distance from an axis which will create rotation that's called torque okay great so Pang if the plane is normal to the flow of electric field that's when the flux is maximum okay flux minimum EPO when when your area vector and electric field are perpendicular so fluxo yo zero when your area vector and your electric field are basically perpendicular okay great so let me see how many of you are able to get this correct come on guys I want you all to be fast ahed ahed Vector Basics ahed any Vector is written as magnitude of vector into unit Vector P Vector can as magnitude of P Vector into P CAP basics of vectors see the answer very good aay ad very good arut sent sir Super S Tes rsh fantastic pangla trishant sandya very good sya great great great you guys are epic very good boys and very good girls you are all Epic Kik I will show you check it okay so through a square square of 40 cm so we all know flux is e a COS Theta so e 6 into 10 the power 4 jcap okay jcap along Y axis so electric field along Y axis Square it is at an angle of 60° to the x X Y plane sorry x z plane so 60 60° now then it makes 60° with our it makes 60° with our with our electric field okay the flux of this peel through a square of a side 40 cm whose plane is inclined at 60° to the x that plane X plane now so you have X axis and Z axxis so on the plane x z plane so x z plane it is inclin at an angle of 60° are you all clear my dear boys and girls are you all happy very good so area area is square 40 into 40 and C of thetaa important Theta area electric Vector electri so Vector will be0 only you have to visualize so electric field it is along y AIS and plane it is along XZ plane so XZ plane it it is making 60° so you have to visualize a little so X 60° now electri it will make I want you guys to slightly visualize try to go and useing softwares okay I hope all of you will get it easy the answer is 4, 800 40 by and C of 60 is 1x two so C of 60 1X two P if you simplify it you will get 4,800 Newton M Square per Kum that is the answer are you all clear everybody happy s everybody cool with this great Superba okay so now let's move forward so it is a very useful it's a very useful law to find out electric field we will derive electric field because of long infinite wire we will derive the electric field because of a plain sheet which is infinitely long we will derive the electric field because of a thin spherical shell so in the my derivations useful so the total flux the total flux enclosed is equal to charge the total flux is equal to charge enclosed by Epsilon KN go statement enclosed by Epsilon as per the GS law the total charge enclosed in a closed surface is proportional to the total flux total flux enclosed by the surface so G line charge enclosed by a closed surface is proportional to the total flux enclosed by the surface so equality Q is equal to 5 into Epsilon so 5 is equal to Q by Epsilon I hope all of you are aware of this easy okay so the total flux enclosed by a closed surface is equal to the charge inside the surface divided by Epsilon what is Epsilon not Epsilon not is the permitivity of free space very good so that's it important I'm going to go through it going go through it quickly so I will repeat God the total flux enclosed by a closed surface Clos surface you can choose any closed surface you can see here the gajian surface can be of any shape no matter what shape and what size so Garian surface is your wish you can take however you want you can take however you want so any gajian shape shape or Surface you take the flux total flux enclosed is equal to charge within that surface and the surface k a charge divided by Epsilon useful to derive electric field for so many cases which which we will derive now which we will derive today okay so the in the r Point Muk regarding Goa please go through it G Law is true for any closed surface no matter what shape what size that's the first point R the term Q on the right right side is what the term Q on the right side flux is equal to Q by Epsilon so the term Q on the right side of G Law what does it mean it is the charge enclosed it is a charge enclosed number Clos surface charge number Clos surface charge charge enclosed so you include only what is present inside it can be present anywhere inside but it has to be inside Pur are you all clear Dar very good D March five is good that gives you a lot of time for revision so yes that's a good plan go ahead okay great in the situation when the surface is ch that there are some charges inside and some outside the electric field is due to all the charges both inside and outside but the term Q is only enclosed charges is because of all of them I want to find electric field because of all of them so you will find electric field because of all of them effect it will come God's it is so so powerful okay so electric electric electric field you want you want the electric field because of all of them what is inside what is outside the fi because of all of them but even then on the right hand side whatever Q you will put it is Q enclosed so Q inside the surface so you will put Q13 Vish you will get the effect of that also it will be automatically taken care of that is what Gola is so famous for sir Q3 right side we use only Q enclosed only enclosed charges so that is what the third point is saying I hope you understood now moving on fourth fifth and sixth point the surface that we choose for application of go law is called as the gajian surface so goian surface it cannot pass through discrete [Applause] charge so Q3 Q Gan surface cannot pass through a discrete charge yeah Char electric field is very high K by r s what is electric field electric field is KQ by R squ so when R is very very small R is like 0.001 R 0.1 so it'll be difficult to deal with it okay it is not well defined when you cross over that so so you cannot pass your Gan surface through a discrete charge okay Point Gau law is often useful towards a much easier calculation of electric field we will choose a very nicean by using symmetry if you can find some symmetry you will try to use it and that will help you to derive it faster to derive it easier and last point is nothing it's very simple go C laww is based on the inverse Square dependence on distance which is contained in your kums law so any violation of God's law will also violate your kums inverse Square law so go is perfectly fine it is valid and we will use it to derive things lastation I hope all of you are ready yes everybody up for it great great great so thin sperical shell we get KQ by R square which is again proving your inverse Square relationship inverse Square relationship of your field with distance so if you are asked to prove what it means okay so pangla now let's try to solve this electric field due to a uniformly Charged long wire so pangla if you have a uniformly long wire infinitely long wire then we take charge density what is Lambda Lambda is linear charge density okay so Lambda is linear linear charge density charity why we take Lambda why we take Sigma surface charge density volume charge density linear charge density now I hope it makes sense okay so we have a infinitely long wian surface is going to be a cylinder so I'm going to choose a cylinder as the Gan surface do you all agree are you all happy so in the infinitely long wire electric field will be radially outward do you all agree the electric field will be radially outward or Infinity long wire the electric field will be radially outward at every point do you all understand that are you all able to follow what I'm saying yes so in the top C bottom top botom can you all please let me know sir top bottom zero sir sir area Vector is Mal outward and electric field is radi area is perpendicularly outward outward Normal area Vector is outward normal noral so it is outward normal and electric field is radial so R 90° so flux because of top Circle and bottom circle of the cylinder is mutai Masa did you all enjoy it are you all clear are you all happy how are radially outward Sanjay because of a infinitely long wire the field is r outward it's a known fact man okay because it is uniformly charged how can it be in any other direction yup okay it's a uniformly Charged infinitely long wire so it's going to be always radially outward okay and pangla it will depend on the radial distance so radial distance the value of electric field will change so RC field coming so if you are having at a constant distance sir number wire length at a distance R the magnitude of electric field for all those points will be equal do you understand that do you understand that so if you if you take the distance to be R from the center from the from the wire the direction will be rad outward will be rad outward are you all clear so I want to apply G Law total flux is equal to charge enclosed by Epsilon KN okay do you all understand that this ccle ccle surface area correct curved surface area so curved surface area sir curved surface area 2 pi r l l is the height of the cylinder R is the radius L is the height of the cylinder 2 pi RH CSA curved surface area of a CS of a cone is 2 pi RH H is L in this case I have taken the length of this the height of the cylinder to be L okay are you all clear so curved surface area into electric field why because everywhere in the CSA the area and electric field are parallel correct so cylinder so is outward area is rad outward electri field so electric field radially outward area radially outward so area and electric field both are parallel so cos Theta is zero Theta is zero cos Theta is one okay so area into electric field and cos Theta is cos0 which is one so this is my left hand side this is my total flux do you all understand do you all understand how many of you are happy did you all enjoy it so this is the total flux on the left hand side now charge enclosed charge enclosed this what do we have here sir in Lan surface the length of the wire is L so how much charge is there lamb number linear charge density so it is going to be Lambda L by Epsilon Lambda is the chared Lamb divid by Epsilon canc it's very easy so what is the electric field electric field is Lambda by 2 pi r Epsilon KN so this is your electric field which is R outward from The Wire Mass V level it's too good too good a derivation I hope you all enjoyed it I hope you all able to follow okay so last en enan surface so we are looking at linear charge density because it's a infinitely long wire so that's why you have to look at linear charge density so linear charge density is what Lambda so sir Lambda L is the charge which is going to be present by Epsilon KN that is equal to total flux total flux surface surface what is the total flux through through the upper Circle and bottom Circle it's and electric field is left so they normal outward area Vector is normal outward so area Vector is normally outward and electric field is radially outward so normally outward radially outward 90° so it is zero because cos 90 is zero so in the in the surface in the surface M so curved surface area so curved surface area we know it is 2 r for a cylinder and luckily curved surface area electric field both will be in the same direction both will be in the same direction electric field is radially outward and area radially outward because area is outward normal always remember area for any surface direction is outward normal okay great super so I hope all of you are able to follow so electric field is equal to Lambda 2 pi r Epsilon so I can multiply by two divide by two so I'll get electric field is equal to 2 K Lambda by R so this is the formula for electric field so it is varying 1 by R so it is varying inversely 1 by R okay so for a long wire in initely long wire the electric field as you move away it will vary as inversely as 1 by R okay P are you all able to understand very good super so I have explained literally everything okay it is because of the entire wire the electric field is because of the entire wire the infin long wire that is the beauty of God's law even though you take Q enclosed you still get the electric field because of the entire thing did you enjoy it okay I hope all of you are able to understand so now we shall move forward at the deration so guys what is the answer here can anybody let me know quickly what is the answer very good super super you guys are correct so answer electric field just now we studied for a uniform linear charge infinitely long wire infinitely line of charge okay so that is going to be how much we know that it is 2K Lambda by R so 2K for a medium it's a constant so e is proportional to Lambda by R okay so Lambda by R is the right answer you guys are absolutely correct let's go we almost done we are going to hit four hours I think four five hours is my maximum so yeah let's let's try to finish it off and maybe we can solve questions tomorrow in the chapter based questions we will try to solve it okay so electric field due to a uniformly Charged infinite plane sheet so the pl sheet the pl sheet okay so you have a uniformly Charged plane sheet in the plane sheet it is infinite so you can keep extending it it's going to be extending up to Infinity so in the plain sheet electric field so you can use a cubid or you can use a cylindrical Gan surface I think ncer they have used cuboid if I'm not wrong ncer I think they have used cuboid if I'm not wrong yeah see ncrt they have used cubid if you look at page number 34 they have used cuboid but I'm using cylinder okay almost the same deration so conf okay surface you can take you can take any shape any size it doesn't matter it will still give you the same result okay so so in the case in the case I want everybody to answer I want everybody to answer what is the flux through the curved surface area so flux through do you agree very good arut sent mesh Kumar super very good so curved surface are sir yes sir area will be radially outward and electric field will be like this so electric field because of a infinite plane sheet will be to the left and right okay so electric field because of this plan sheet will be like this so that is how the electric field will be like it is an infinitely long plain sheet we had a line charge line charge we saw electric field again like that sheet it will be to the left and to the right okay are you all clear everybody happy with this shall we proceed everyone quick quick quick quick great so so curv surface we have this and this your electric field is also left and are is also left electri told plain sheet if it is positively charged left side it will be leftward right side it will be rightward positive charge will repel so that's how electric field will be positive charge away positive charge away so in the electric field is like this to the left and in the surface normal outward normal is also like this so what is the flux flux is EA e is electric field mag magnitude and a is the are of the surface e is outward and area is also outward the flux is EA sir plus EA is 2 EA so total flux so that is my total flux so total flux is equal to charge enclosed what is charge enclosed charge enclosed is Sigma a charge enclosed surface charge is Sigma into a sigma surface charge density divided by Epsilon KN so you can find out AA cancel so electric field is Sigma by 2 Epsilon KN such an important result please note it down such an important result please note it down okay are you all cool with it great so let's go ahead and solve some questions please try to solve it the answer is option C yes option C is correct it has no dependence on R the electric field is Sigma by 2 Epsilon so Ang there is no R term Sigma is your surface density and Epsilon is a constant your pertivity of free space okay so Sigma by 2 Epsilon does not have R so it is independent of R that's that's a beautiful result okay so the last derivation AR because of a thin spherical shell so the last derivation last 10 minutes we are almost done my throat is gone okay so electric field due to a thin spherical shell so let's say you have a thin spherical shell like a Hol spere basically okay so you have a hollow sperical shell like that you have and you want to find find out electric field at a point inside okay so let's say I want to find electric field at this point electric field at a point P the point I will take aian surface a sphere basically so I will take a gajian surface which is a sphere basically okay so now I'll apply Gau law what is gosla gsla is total flux enclosed by the Garian surface is equal to charge enclosed charge enclosed by Epsilon KN so flux sir because of positive charge you will have field electric field which is going to be radial electric field is going to be radial and your area is also radial your electric field is radial and area is also radial okay so what is the what is the flux the flux is going to be electric field into area see E and A are same direction so total area total area is 4 pi r squ where R is the radius of the gajian sphere gajian surface okay that is equal to charge enclosed is mutai by Epsilon KN so because of this your electric field will be zero so electric field inside electric field inside uh sperical shell is M got it did you all like it so will you will get total flux because total flux is e da ch flux added together da Direction both are radial so Theta is zero if Theta is zero this will become Eda because e daa cos Theta Theta so cos Theta will become one so now at a radial distance of R electric field everywhere is constant at a radial distance of R because we know spere radial distance electric field same electric we canate da so sir D integrate you will get total surface area total surface area is 4 r s you should understand got it okay I hope all of you are able to follow that's it Z anyway charge enclose zero in the in the Gan surface en so in thean surface the Enos is you get electric field zero I hope you got it last deration last slide yes almost done okay electric field due to a thin spherical shell for a point outside so easy for a point outside what is the total flux Reas see Point outside thin spherical shell so Point outside at a distance of R so Gan surface so my Gan surface is a sphere of radius small R it's a sphere of radius small R okay so law total flux is equal to charge enclosed divided by total flux is equal charge enclosed by Epsilon flux flux is e a COS Theta so total flux is nothing but e into 4 r² so total flux e into 4 r s because e both are radial sir it will become e cos Theta and what is Theta dire sir Theta zero one one it is integral at a radial distance of r r r electric field constant so electric field magnitude will be same Rance magnitude of electric field will be constant I can bring e outside so e into integral da what is the integral of all the area along this surface surface area so e into surface area is e into 4i R square because 4 Pi R square is a surface area of a sphere that is equal to charge enclos charge enclos is the full Charon so eal 1 by 4i r² Epsilon Q so it is k q by r² so this is the electric field because of a thin spherical shell so or thin spherical shell for a point outside you can treat it like a point charge level so even though it's a thin sperical shell and you finding it at a point outside it is treated like a it is treated as though you have a point charge Q Ilia isn't that right so in the sperical Shell where Q charge is distributed Q charge is distributed along the shell along the sperical shell electric field at p is same as a point charge at this point having electric field at here both are same so you can treat a thin spical shell for a point outside you can treat this as a point charge okay so yeah that's how Pang over we have completed the entire chapter luckily fortunately okay so all the very best I hope you enjoyed it so in the session so please do share it to all your classmates Juniors so thank you so much and I will give it to you please wait for it okay so group please do join it for updates some of you are returning back and some of you are new to the channel so please make sure you subscribe share it to your friends and if you enjoyed the video leave a like leave a comment that would make my day so take care all the very best love you all see you tomorrow with another epic session I will keep it a surprise take care guys bye-bye