Understanding Electric Charges and Fields

Hi everyone, today we are going to see an important video. To both the standard physics and board exam is going to take place. For that we are going to do fast recapitulation for each chapter. So if you can quickly cope up with me, we will see how each chapter is short and crisp. So in the first chapter we are going to see electric charges and fields. This is a very important chapter. Electric charges are of three kinds, one is positive and the other is negative. The other is called neutral charge. When we talk about charges, we are going to talk in detail about what kind of electric field and forces are in a rest position. Similarly, when we talk about positive and negative, we know that it attracts each other. Similarly, if I have positive and positive or negative and negative, what will happen to me? Both these will ripple and these will ripple. So, like charges will ripple and unlike charges will attract. And similarly, we have talked about an important thing here, transfer of charges. So, we are transferring the charges in three different methods. So, charges are... We transfer in three methods. So in that way, first thing is we call it conduction. Second is friction. And third is induction. So what we are going to talk about here is for conduction, when we place a charged object over an uncharged object, if we touch both the objects, the charges are equally distributed. For example, For example, if this has 5 coulombs, then this object does not have any charge. But if we touch these two and take it, this will also have 2.5 and this will also have 2.5. So, we call conduction of transferring charges by touching an object. Next is friction. So, we know that friction is by rubbing, we transfer the charges from one object to the other. We have given many examples. For example, we rub silk cloth in a glass rod. For further, we rub it in a plastic. In all these places, charges are transferred from one object to another. In the case of glass rod silk, glass rod is acquiring positive charges. In the case of plastic, it acquires negative charges. So charges are transferred from one object to another. This is done by rubbing. Rubbing is done by friction. We have seen the example of comb. We rub the comb on the dry hair and place it on a paper. it sticks. So what we are trying to say is that electrostatic force is very strong than the gravitational force which we want to describe here. For example, when we say electrostatic force we know that that is K times Q1 Q2 by R square. And similarly when we say gravitational force we say G times M1 M2 by R square. So what is the difference between these two? When we say electrostatic force, we consider the charge and gravitational force we consider the mass of the object both are inversely proportional to the square of the distance between them here is a constant, you know here is a constant, we know that too this is gravitational constant and this is electrostatic constant so charges by rubbing, we say it is a friction process next is electrostatic induction so induction means charges without touching charges from one object to the other object So this is a positive charge object and this side is a When we touch these two objects, the charges are equally distributed. So, the positive and negative charges are equally distributed. We will bring another object here. If that object is negatively charged, what will happen when we place it next to it is, in this object, all the negative charges will go to that side, and this side will get full positive charge, and opposite side will get full negative charges. Because this is negative and this is positive will attract each other. This is negative and this is negative will ripple each other. So after that, we will take this, or we will separate these two, and when we take this now, this object will get full positive, and this object will get full negative. So initially, I had equal amount of charges. After that, it is just a positive and negative conversion. So how do charges transfer? Without touching. So that process is called induction process. Next, we have conductors and insulators. So what is conductors? So basically, we are studying conductors from 9th standard. So when we say conductor, free electrons will be more. In insulators, free electrons will be less. So what is conductors? If it is high, free electrons will be more which is low resistance. In insulator, free electrons will be less which is high resistance. So this is the basic difference between insulator and conductor. Next is, when we stick a plastic comb on our hair and it attracts. So instead of using plastic comb, we can use iron. If we use iron comb, will the process happen there? Will the paper get attracted there? If we ask like that, it will not happen. Because our human body is a conductor When we wrap, even though the charges are created there it will transfer to our body But when we wrap it in plastic the charges will not get distributed in the plastic It will be there in the same place because it is an insulator, the charge will not move If it moves in the conductor, it will come to the body So, we can say that. this is the basic hint given to us so next we have additivity of charges or basic properties of charges so when we say basic properties of charges we have 3 different things so in that we have additivity of charges second is conservation of charges third is very important quantization of charges so I did Additivity of charges is, we add the charges, so magnitude plus direction, either it is positive or negative, we just add and we get the net charge. So that is addition of charges. So conservation of charges, I cannot create or destroy charges, but when I say a system, charge remains the same. For example, here I have an object, this is 5 coulomb, here I have an object, this is 2 coulomb. Now what happens is, we touch these two objects here. and the charges are distributed evenly so 7 is 3.5 and this object is 3.5 and it splits but if you look at it carefully, the initial charge of these two objects is 5 plus 2 is 7 after touching, the charges are transferred and even now it is 3.5 plus 3.5 so the whole system is before transfer of charges is 7 and after transfer of charges is 7 so the whole system charges remains the same so the whole system charges remains the same That is what we are going to talk about as conservation of charges. Next we have quantization of charges. This quantization of charges is just the integral multiple of charges. So, Q which is equal to n times E. N stands for number of electrons. Either it can be 1, 2, 3, 4, 100, 1000, 1000, lakhs. E is the charge of one electron which is nothing but 1.6 10 to the power minus 19 coulomb. So, this is the charge. right so which mean quantity of charges of the number the quantization of charges and so quantity of charges because I'm a sofa run there in the object trigger my touch ponder or a ponder or induction process and the charges transfer of the yellow transfer of the I'll be in the quantization of charges we can easily find so Q which is equal to n times e I've been so long if I want to find number of electrons of Dina I can also rearrange the formula like this Q by e of the end of the end of the number could market so even the Pokemon So number of electrons I can easily find if it is one coulomb of charge How much will I have in one coulomb of charge? This is nothing but 6.25 x 10 to the power 18 So we need to know that I have so many electrons in one coulomb of charge Similarly, if I have only electrons and protons, then it is not possible Many kinds of charges especially positive charges and negative charges are always present in any kind of objects. So positively charged means negative charges are less and negative charges are not. Negative charges are more and positive charges are less. So how I can write quantization Q which is equal to I have proton and electron. So I can also rewrite this as proton electron which means the charge plus I have electron. this NP and here minus E because to represent the charges I have written plus for proton and minus for electron so how I can write this is electron right so I can also say this is NP minus NE to the product of E even here this is nothing but the integral multiples anyhow you can separate it either it can be 1,2,3,4,5 it can be any number like that only 1.5,2.5 will not be there because we cannot split cannot break the charges of the interstellar more solar power so you know the other way up to make whole number of the you cope right so you're going to quantization of charges when the soldier the you know simple as alone of the area it increases or it decreases step by step although the eternal economy in the middle of body of Panna Cuddy a wish you so I don't the number come on the the electrostatic rate so either part of the next topic number can Eric next topic on the patina coolums Larry So coulomb's law is a very simple conceptual base. So what we use coulomb's law for is to find the force between the charges. We use coulomb's law to find the force between two charges. Whether it is positive or negative or positive or negative. So how are we going to define this coulomb's law? F which is equal to K times Q1 Q2 by R square. Right, this is our electrostatic force. and then the gravitational force becomes g times m1 m2 by r square so here we know the value of k is 1 by 4 pi epsilon naught r and epsilon naught r since it is placed in vacuum and air its value will be 1 we have discussed this in detail and this is nothing but 9 into 10 to the power 9 newton when my charges are 1 coulomb and its distance is 1 meter and the value of of f and they will be equal to k so f which is nothing but 9 into 10 to the power 9 newton so this is called coulomb force this is also inversely proportional to the square of the distance between them product of the charges and there is a constant also which is k that is the value of this or you can also say epsilon which is equal to epsilon naught and epsilon r we can very simply represent this since we have r this value is 1 relative permittivity So, we are not including in all the terms. That is one thing we need to understand here. So, this is the Coulomb force. How can we call this as the Coulomb force in the vector form? If you see, the vector form is very simple. Right, now let's say I have a charge here and a charge here. Let me say this is Q1 and this is Q2. Now, this charge can give a force over this. This charge can give a force over this. Because it is similar charge, there is a Represive force. So this gives a force on this and this gives a force on this. So how I can represent the coulomb's line in vector form is, let me say F1,2 is force on 1 due to 2. Who gives the first charge? He gives it. So force on 1 due to 2. So K times Q1, Q2 by R. R is distance. R square. Where does it come from? Electric field. Who gives the force on this charge? It comes from here. So R21. Right? R21. So here R cap R21. Very simple. When we say F21, F21 means force on charge 2 due to 1. Where does it come from? This charge comes from here and this comes from here. 1 to 2. So how I can write K times Q1 Q2 by R square. What is it? Where does it come from? It comes from 1. So R cap 1 2. Very simply our vector form is solved. This is possible only if there are two charges in the coolums. Now I have multiple charges. So what I can do in that place is, I can go with the Superposition Principle. So here comes Superposition Principle. So, super positive principle says that I have multiple charges. I don't have two charges. So, if I have multiple charges, it is like this. So, when we have multiple charges like this, we can consider this charge and say what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, we just add. So, this one charge, let me say this is Q2, Q3, Q4, Q5, Q6 and Q7. So, let me say that is Q1. So, how can I say, how I can represent my force? What force? which is equal to K times Q1 and Q2 the distance between them is 1 to square the distance between these two charges so this is 1 to square. When we say 1 and 6 I have 1 and 6 here. So that is K times Q1 Q6 divided by R square that is the distance between 1 and 6 So this is how we find the force of each kind of charge Then we just add F total When we say F total, I get K common everywhere and Q1 is also common so K is common, Q1 is common what we are adding? summation of QI that is 123456 that is what we are adding so that is I can say that this is from 2 to I similarly we have distance this distance also changes so charge from 1 to n number of charges so you can also say I square so this is multiple charges this is the way I can find my total electrostatic force so next to that this coulomb force and multiple charges we have electric field electric field is another important concept we have to see here so electric field so basically what we know I will sum up all these and finish here so electric field is given or it is coming out from or getting in from negative and positive positive charges so positive charges so the electric field is ready output negative charges so the radio input then the charge will be pocket alert so we have a attractive force which is due to the electric field which is present on this particular charges so either another than I come to the repulsive force over to the attractive force of your copy the momentum so how we can represent in mathematical expression of the party which is equal to F by Q I mean so so for acting per unit charge if I don't want the source charge every now and then the point point charge and the point charge right in the point charge in the electric field I just go with the point charge so in the point charge test charge we always go with the positive charge because in order to find their effect so how the effect is we always go with the point charge and test charge right so we use test charge to test the charge very simple So, there is an electric field. So, when the electric field acts at this point, how much force can be given to this? That is what we call electric field. Electric field is the force per unit charge. Similarly, when we say positive, the electric field of this also will be affected by this. But, the amount of charge value of this electric field which is not there, is almost 10 to 0. That is what we have said in our book as limit and Q 10 to 0 F by Q which is nothing but electric field. So, this is the meaning of this. The meaning is, to prevent the electric field from coming from the test charge, if we take this value as 0, the effect of this will affect it completely. To indicate this, they have mentioned this. But also we can also rewrite this as kQ by R square. Because when we say electrostatic force, it is the force between the two charges. So Q1 and Q2 by R square, by this Q, one Q and this Q will get cancelled. Which is nothing but kQ by R square. So in the other term, I'm... The important thing to note is that we have not considered the test charge. That is what we have cancelled. Without considering the test charge, we have taken the source charge only. So, F which is equal to, sorry, K which is equal to KQ by R squared. Very simple. So, what is this? There are two charges. Suppose, here I have multiple charges. Right, multiple charges. So, this is similar to... That superposition principle. So, when we say first, what we found? F total which is equal to kq, which we have summed up and divided by 1 i square divided by 1 i square and from 2 we have i. force superposition principle here electric field is same as E total which is equal to same way I have found electric field in two charge fields then we add so in this K is the only common nothing else is common and also source charge is also common source charge is also common so what will change for me distance will change so from 1 to I distance will change so summation So that's all we are going to talk about electric field. And similarly, we will be given another basic understanding part of electric field. So this is positive charge and this is negative charge. So electric field is all radially outward. To understand this, my strength will be higher near this charge. the distance will decrease as we go that is what we call electric field which is equal to kQ by R square when the distance increases the electric field strength will decrease we can easily understand this here similarly as the distance increases area for 3 electric field line also increases. So in this way, I have these three electric fields. When the same distance increases, see how big the same three electric fields are. So I can also say that my strength strength is directly proportional to distance and the same distance is directly proportional to area. So area is directly proportional to distance. So this is a basic understanding. Next we have dipole. Dipole is not a concept. for that we have electric flux electric flux so electric flux up into the electric for the number of right number of electric field line crossing in a given area electric field line goes and that defines my strength. So, how do we define electric flux? Electric flux which is equal to E ds cos theta. So, when my angle is 0 degree, it will be maximum. And when my angle is 90 degree, it will be minimum. Why? Because when my area vector and electric field are 0 degree, my flux becomes maximum. When my area vector and electric field are 90 degree, this becomes minimum. So, this is the reason why we call it electric flux. we will use this concept after that we have another concept dipole, when we say dipole we have equal charges, the charge magnitude will be same direction will be opposite electric dipole two polarities two polarities, one is positive and the other is negative distance at the company now in the midpoint learning the inner echo idea the in gear right up easy a up in a easy a bina in a total distance in the core to a up in a record and I the mother in a dipole moment direction patina negative to positive right dipole moment or the direction patina negative to positive so la electric field a direction patina positive to positive to negative so electric field a direction positive negative dipole moment a direction negative positive so in the dipole the net charge you have to remember always so net charge of dipole that is equal to zero net right net charge total charge because this is also plus this is also minus both are same now 5c is also 5c this is plus 5c this is minus 5c so total net charge in a given dipole when we talk about this the value always becomes zero because both are same we add it will be zero net charge additivity of charges right So this is a small understanding. So in this we have given another case. What are the cases? In this itself we have given an Axial case. Next we have Equatorial cases. So here I have a positive charge, here I have a negative charge. The distance to be put in this is a. So the total distance is 2a. Now I am choosing a point. The distance to this point and this midpoint is R. Now what I am going to do is, at this point. What electric field can be given by these two charges? So we know what electric field is. So far we have learnt electric field which is equal to force per unit charge or kq by r square. When I get positive charge, my distance from here to here is only this. So my distance is this a, this is r, so I don't need a. So the distance of this is r minus a. Correct? So, this distance, this charge, this is R and this is A. So, this is R plus A. Correct? R plus A. So, this is very simple. So, what we are going to do? If it is a positive charge, what I am going to write is KQ by R. R is the distance between the positive charge and the positive charge. So, R minus A is the whole square. Right, so this is positive charge. Now, when I say negative charge, it is kq by r square. Here, k, q is negative charge, so minus, right, so minus by distance. This distance is r plus a. r plus a is the whole square. Right, now what I have done is, I have found out two electric fields. What I am going to do, I am going to just, I am going to total it. So, when I total, what will come? E total which is equal to, do I have kq in these two places commonly? So, KQ is 1 by R minus A the whole square. Right, R minus A the whole square. This minus is there. So, minus R plus A the whole square. Correct? Now, what I am doing is, just crossing it. So, KQ. If this is different, just expand A plus B the whole square for a while. R square plus A square plus 2AR minus F. If this is different, R square will come. Since there is a minus here, minus R square. a squared will be plus, because of taking a minus here, it is a squared. minus 2ar will be there, because of taking a minus here, it is plus 2ar. whole divided by r squared minus a squared, the whole squared. In this point, we have a very simple understanding. This plus and this plus, this minus and this minus will be cancelled. So the remaining term is k cube, what is this? 4ar divided by, my a is r squared minus a squared, the whole squared. Since my r is bigger than a, I neglect the a and take only r. Right, I neglect the a and take only r. If I take only r, it will be 4 to the power of r. The r here and the r here will be cube. So this is nothing but 2 into 2. So what can we do? 2. 2aq is dipole moment. So what we can do is, there is a 2 here, dipole moment is k by r cube. Okay, so this is the basic understanding. So we have already told dipole moment here, so 2aq is dipole moment. So next we move to equatorial concept. So equatorial concept is a simpler understanding. Right, so Equatorial. So Equatorial means I have two dipoles. The distance between the two dipoles is A. The total distance between these two is 2A. So I am going to choose my point in the bisecting point. When I say Equatorial, I mean the midpoint. point from both the charges. So let me say this is the distance, this is the charge, this is the point, this distance and this distance are the same. So this is positive and this is positive, so this is the force impulse. this is negative and this is positive so the force is like this so the resultant force is here and here so we have two different components, one sign and one sign both are opposite so it is cancelled, we have one cos theta so this has one cos theta and this has one cos theta so there is a cos theta in plus charge and a cos theta in minus charge so what we are going to find is the total electric field so I need every electric field if we have to pay attention here, I have said that I will measure this distance he is checking the distance I need Right, so E is the force per unit charge or kq by r square. So, r is the distance between the two charges. So, we know the value of k, and the value of q is the charge, obviously, positive charge. R is the distance between the test charge and this. So, if this is right angle triangle, this is opposite, this is adjacent, and this is hypotenuse. So, when I say hypotenuse, I can also say that hypotenuse square which is equal to opposite square plus adjacent square. Now, please do that again. distance hypotenuse square than a square than a upon just writing R square plus yes they're almost implementers right number simple move square the head hypotenuse square the square now other than a bridge so you know negative charges alone will either work with you in the changes are today which is equal to K negative charge divided by R square plus a square yeah you know you know you know you know you know you know you know you know you know you know you know you are in you so same of being another I'll be having the same thing again our caner cast it are copying here in the corner cost it a no you give her a cost it a no right if I don't know I'm going to add it up a total which is equal to render the limit here Q okay up around the R square plus a square okay I think I'm going to do a cost it over okay up a how I can write I can write this as 2 times KQ So, cos theta is opposite by hypotenuse. Right? So, opposite by, sorry, adjacent by hypotenuse. So, cos theta, which is equal to, right, this is the angle, adjacent A by hypotenuse. Hypotenuse is not hypotenuse square. Hypotenuse. This is hypotenuse square. So, root over comes. So, R square plus A square. Root comes and 1 by 2 is written. I wrote one by one. So we will substitute this value here. Which is equal to 2 times kq by r square plus a square. Here it is a divided by r square plus a square. 1 by 2. So this is 2 or same. This is 1 by 2. Which is 3 by 2. Now if I write like this. 2 aq is p. k. There is a negative sign. Don't forget. And here r square plus a square. 3 by 2. Similarly, my r distance is very big when compared to a. So, if we neglect a, what we have r square into 3 by 2. If 2 is big, then it is just r cube. So, Pk by r cube. I get negative here. Why I get negative? Because my dipole moment and electric field direction are opposite. So, my dipole moment is negative to positive. This is how dipole moment is. Electric field is like this. Both are opposite. We are just mentioning this as negative. that point has a mark, so make sure that you are mentioning that also right, so this is also done for us so what are we going to do after this? right, so the next concept we have is Axial Equatorial and after that just seeing the topic, we should know right? next we have a Dipole right, so dipole in an electric field What will happen when we place the dipole in electric field? When we place the dipole in electric field, a very simple thing will happen. So, I have positive and this is negative. The distance to this is a and the total distance to this is 2a. So, if I place it in... electric field. Right, if you see here, the electric field is like this. So this is positive. Obviously, what is this for me? This is positive for me and this is negative for me. Both are like this. Both are in opposite directions. My net force is zero. This is a very important point. net force on the another zero on our neck in the little in a rotating effect on the neck rotating effect on the get possible up in the other we are just a mentioning dark right so dark which is equal to force into distance so your force in electric field in the charger so we know that electric field up into the force per unit charge up of force up into the end the cube to produce a Q times e up a Q times either in over here first so distance between the diaper which is nothing but 2a and this is my maximum and my dipole is like this and my electric field is like this so it is 90 degree so just write sin theta or you can also say 2aq is nothing but p right or pe sin theta or you can also write p cross e in vector form very simple so this is when it is 90 degree 0 degree is minimum 180 degree is minimum, that is, parallel to the dipole moment of electric field is minimum. Anti parallel, that is, 180 degree is also minimum. When is this possible? When there is a uniform electric field. The next concept is about continuous charge distributions. Continuous charge distributions. We can also go with three important terms. So one of them is linear charge density, lambda. the Q by L other the straight wire of the density of the charge of the either solo or you can also say Q which is equal to lambda L even the surface charge density other most sigma and solo Q by a or you can also say Q updated on the here depends on so a Sigma Sigma if it is a volume you can also say Q by volume or you can say Q which is equal to rho V is a little bit So this is linear, this is area, surface area, this is volume charge, density. So this is it. So the concept we have is based on this in Gauss law. So what I am saying in Gauss law is, So, in gas electric flux is equal to EDS. Right? EDS is cos theta. So, here I have a sphere and this sphere is positively charged. So, what happens is, there is a charge inside this and this is how the electric field is. Because the... So, the area vector of each surface will be like this. The area vector of each point will be like this. Right? So, the area vector of each point will be like this. The electric field will be like this. Right? Each and every point of the area vector and electric field will be in the same direction. Which makes the angle to be zero. So, if I do that, cos theta, cos zero degree is equal to one. So, EDS. So, flux is equal to EDS. Right, E ds is what we can say. And also we know that electric field is KQ by R square. ds is the area. This is the sphere, or surface area, which is nothing but 4 pi R square. If it has radius R. So what I am going to do here is, I am just substituting K, what is the value? 1 by 4 pi. epsilon naught, I have this q, this r square, this 4, this pi and this r square. and there is epsilon only. So electric flux which is equal to Q by epsilon naught. This charge should be inside the closed surface. These are the important conditions mentioned in Gauss. We can write it like this. So followed by that, we have 3 kinds of applications. One is a straight wire. There is a straight wire. In that straight wire, how my electric field will be. We are going to use that by using gas lava. This is the wire. This wire is full of positive charge. So how will the electric field come out? It will come out like this. The electric field will come out like this. Now I have to find the electric field in this. All these are continuous charge distribution. So discrete means isolated charges. Multiple charges, coulomb, forces, superpowers, principle, all these are isolated. Like discrete charges. I don't have discrete charges in nature. All these are continuous charge alignment. So this straight wire has n number of charges. And the directions of the electric field are positively or negatively outward. Now what I am going to do is, I am just going to imagine a circular thing. Right, so what I am going to do is, I am going to choose a point and the point will be like this. distance is order a the number of points and I'm making this as a closed one right is there a closed cylinder as important right up in the earth in a party now he put in the in the bottom surface is the bottom is the area vector the surface in the middle of the day you can also able to understand the electric field of the degree so flux of EDS cos theta, EDS cos 90 degree, cos 90 degree becomes 0, the whole term becomes 0. And here also 90 degree, here also whole term becomes 0. So where is this curved surface? So curved surface, since it is a cylinder, my area is 2 pi R L. So we have electric flux which is equal to EDS, gas is Q by epsilon naught. Very simple. So for me this E, we need to find electric field which is equal to Q by epsilon not DS so Q by epsilon not since it is a linear charge density the Q what I am going to do is since it is a linear charge density straight to wire so in that place we said Q is equal to lambda L so I said lambda L because it is cylinder what I am saying is its area 2 pi R L L is gone so my remaining term electric field is lambda by 2 pi epsilon not up Very simple. So the next concept is a plane sheet. How will I have an electric field in a plane sheet? So like this we have a plane sheet. In the plane sheet, what I am going to do is, I am choosing a small area. So, I am choosing a small area like that and just writing it. So, I am choosing an area like this on both the sides. We need a very detailed explanation. We have posted a video. also refer that so in the fast recap and I'm just going in so in the other part in the in the over at the limit open area vector go in the area of the record in the area of the record in the area of the computer since it is a positively charged sheet of the eternal a lot of an ing in the area like the electric field a lot of beer electric field a lot of beer correct electric field Allah you put it opening and a lot of a thing in the la service with the underneath the community degrees economic front to back all 90 degree. Where is it? This is 0 degree for me. This is 0 degree for me. So what happens here is that only in these two surfaces, the maximum flux is there. So how I can say electric flux which is equal to Q by epsilon naught, similarly EDS cos theta. So if you see here, in both the places cos theta is 0 degree, but to EDS or E area. So, we have to do ds. There is nothing wrong with that. And then we have a Q by epsilon naught. Since it is a surface, right, since it is a surface, I am just writing. See what I am saying? See what I am saying? I have E like this, right? I will bring 2A here. So, Q by epsilon naught, I have brought 2A here. I have brought 2a only. Since this q is surface charge density, sigma a divided by epsilon 0 2 times a a a is cancelled. So my electric field is nothing but sigma by 2 epsilon 0. This was a plain sheet. Now I want a spherical shell. I have a shell. So, when I say spherical shell, it means how my electric field will be. So, I have a shell like this. What we are going to do is, we have placed the charges inside. So, the charges will be distributed on the surface. There will be no changes in that. Now I am going to choose a surface in the outer side. So I have this charge inside the imaginary surface. So we can able to do. So this is capital R and the distance of this is small r. The distance of the surface. So electric flux is... Q epsilon not I'll be putting a EDS later so since it is a surface charge density you can also mention that s Sigma a by epsilon which is equal to E of in the electric field even a patina sphere surface star so I can also rewrite that as for PE no more in the surface of the circle I'm in the surface of the circle I'm going through the surfaces Liam so you must really This is the charge which we have taken as an imaginary which is nothing but 4 pi r square. So you can also rewrite this as electric field which is equal to sigma A divided by epsilon naught 4 pi r square. You can also substitute the value of A, sphere, that one becomes 4 pi capital r square divided by epsilon naught 4 pi r square. the 4.4.4 so you have Sigma R square epsilon and R square so capital by small so it will correct the the outside inside the shell so I'm gonna go on slide I saw the inside charge here in the mountain surface in the surface choose funding of the collection of it is applicable of the new the gossel so better even okay in the green color than a choose for the kudi and the imaginary surface and I like a charging occur really and the surface of the object lyric okay up it is not possible I'll be getting What can I say? My electric field becomes zero. Suppose if I choose this surface, the value becomes this. Right? Then this R will be replaced by R squared, the distance. If it is on the surface. So, don't worry. I hope there are no doubts. So, we will try to do all the chapters as fast as possible. Thank you. Help others with a smile. Share this with your friends. Thank you.

Hi everyone, today we are going to see an important video. To both the standard physics and board exam is going to take place. For that we are going to do fast recapitulation for each chapter.

So if you can quickly cope up with me, we will see how each chapter is short and crisp. So in the first chapter we are going to see electric charges and fields. This is a very important chapter.

Electric charges are of three kinds, one is positive and the other is negative. The other is called neutral charge. When we talk about charges, we are going to talk in detail about what kind of electric field and forces are in a rest position.

Similarly, when we talk about positive and negative, we know that it attracts each other. Similarly, if I have positive and positive or negative and negative, what will happen to me? Both these will ripple and these will ripple.

So, like charges will ripple and unlike charges will attract. And similarly, we have talked about an important thing here, transfer of charges. So, we are transferring the charges in three different methods. So, charges are... We transfer in three methods.

So in that way, first thing is we call it conduction. Second is friction. And third is induction.

So what we are going to talk about here is for conduction, when we place a charged object over an uncharged object, if we touch both the objects, the charges are equally distributed. For example, For example, if this has 5 coulombs, then this object does not have any charge. But if we touch these two and take it, this will also have 2.5 and this will also have 2.5.

So, we call conduction of transferring charges by touching an object. Next is friction. So, we know that friction is by rubbing, we transfer the charges from one object to the other.

We have given many examples. For example, we rub silk cloth in a glass rod. For further, we rub it in a plastic. In all these places, charges are transferred from one object to another.

In the case of glass rod silk, glass rod is acquiring positive charges. In the case of plastic, it acquires negative charges. So charges are transferred from one object to another.

This is done by rubbing. Rubbing is done by friction. We have seen the example of comb.

We rub the comb on the dry hair and place it on a paper. it sticks. So what we are trying to say is that electrostatic force is very strong than the gravitational force which we want to describe here. For example, when we say electrostatic force we know that that is K times Q1 Q2 by R square. And similarly when we say gravitational force we say G times M1 M2 by R square.

So what is the difference between these two? When we say electrostatic force, we consider the charge and gravitational force we consider the mass of the object both are inversely proportional to the square of the distance between them here is a constant, you know here is a constant, we know that too this is gravitational constant and this is electrostatic constant so charges by rubbing, we say it is a friction process next is electrostatic induction so induction means charges without touching charges from one object to the other object So this is a positive charge object and this side is a When we touch these two objects, the charges are equally distributed. So, the positive and negative charges are equally distributed. We will bring another object here.

If that object is negatively charged, what will happen when we place it next to it is, in this object, all the negative charges will go to that side, and this side will get full positive charge, and opposite side will get full negative charges. Because this is negative and this is positive will attract each other. This is negative and this is negative will ripple each other. So after that, we will take this, or we will separate these two, and when we take this now, this object will get full positive, and this object will get full negative. So initially, I had equal amount of charges.

After that, it is just a positive and negative conversion. So how do charges transfer? Without touching. So that process is called induction process.

Next, we have conductors and insulators. So what is conductors? So basically, we are studying conductors from 9th standard.

So when we say conductor, free electrons will be more. In insulators, free electrons will be less. So what is conductors?

If it is high, free electrons will be more which is low resistance. In insulator, free electrons will be less which is high resistance. So this is the basic difference between insulator and conductor.

Next is, when we stick a plastic comb on our hair and it attracts. So instead of using plastic comb, we can use iron. If we use iron comb, will the process happen there?

Will the paper get attracted there? If we ask like that, it will not happen. Because our human body is a conductor When we wrap, even though the charges are created there it will transfer to our body But when we wrap it in plastic the charges will not get distributed in the plastic It will be there in the same place because it is an insulator, the charge will not move If it moves in the conductor, it will come to the body So, we can say that. this is the basic hint given to us so next we have additivity of charges or basic properties of charges so when we say basic properties of charges we have 3 different things so in that we have additivity of charges second is conservation of charges third is very important quantization of charges so I did Additivity of charges is, we add the charges, so magnitude plus direction, either it is positive or negative, we just add and we get the net charge.

So that is addition of charges. So conservation of charges, I cannot create or destroy charges, but when I say a system, charge remains the same. For example, here I have an object, this is 5 coulomb, here I have an object, this is 2 coulomb.

Now what happens is, we touch these two objects here. and the charges are distributed evenly so 7 is 3.5 and this object is 3.5 and it splits but if you look at it carefully, the initial charge of these two objects is 5 plus 2 is 7 after touching, the charges are transferred and even now it is 3.5 plus 3.5 so the whole system is before transfer of charges is 7 and after transfer of charges is 7 so the whole system charges remains the same so the whole system charges remains the same That is what we are going to talk about as conservation of charges. Next we have quantization of charges. This quantization of charges is just the integral multiple of charges.

So, Q which is equal to n times E. N stands for number of electrons. Either it can be 1, 2, 3, 4, 100, 1000, 1000, lakhs. E is the charge of one electron which is nothing but 1.6 10 to the power minus 19 coulomb. So, this is the charge.

right so which mean quantity of charges of the number the quantization of charges and so quantity of charges because I'm a sofa run there in the object trigger my touch ponder or a ponder or induction process and the charges transfer of the yellow transfer of the I'll be in the quantization of charges we can easily find so Q which is equal to n times e I've been so long if I want to find number of electrons of Dina I can also rearrange the formula like this Q by e of the end of the end of the number could market so even the Pokemon So number of electrons I can easily find if it is one coulomb of charge How much will I have in one coulomb of charge? This is nothing but 6.25 x 10 to the power 18 So we need to know that I have so many electrons in one coulomb of charge Similarly, if I have only electrons and protons, then it is not possible Many kinds of charges especially positive charges and negative charges are always present in any kind of objects. So positively charged means negative charges are less and negative charges are not.

Negative charges are more and positive charges are less. So how I can write quantization Q which is equal to I have proton and electron. So I can also rewrite this as proton electron which means the charge plus I have electron.

this NP and here minus E because to represent the charges I have written plus for proton and minus for electron so how I can write this is electron right so I can also say this is NP minus NE to the product of E even here this is nothing but the integral multiples anyhow you can separate it either it can be 1,2,3,4,5 it can be any number like that only 1.5,2.5 will not be there because we cannot split cannot break the charges of the interstellar more solar power so you know the other way up to make whole number of the you cope right so you're going to quantization of charges when the soldier the you know simple as alone of the area it increases or it decreases step by step although the eternal economy in the middle of body of Panna Cuddy a wish you so I don't the number come on the the electrostatic rate so either part of the next topic number can Eric next topic on the patina coolums Larry So coulomb's law is a very simple conceptual base. So what we use coulomb's law for is to find the force between the charges. We use coulomb's law to find the force between two charges.

Whether it is positive or negative or positive or negative. So how are we going to define this coulomb's law? F which is equal to K times Q1 Q2 by R square.

Right, this is our electrostatic force. and then the gravitational force becomes g times m1 m2 by r square so here we know the value of k is 1 by 4 pi epsilon naught r and epsilon naught r since it is placed in vacuum and air its value will be 1 we have discussed this in detail and this is nothing but 9 into 10 to the power 9 newton when my charges are 1 coulomb and its distance is 1 meter and the value of of f and they will be equal to k so f which is nothing but 9 into 10 to the power 9 newton so this is called coulomb force this is also inversely proportional to the square of the distance between them product of the charges and there is a constant also which is k that is the value of this or you can also say epsilon which is equal to epsilon naught and epsilon r we can very simply represent this since we have r this value is 1 relative permittivity So, we are not including in all the terms. That is one thing we need to understand here. So, this is the Coulomb force. How can we call this as the Coulomb force in the vector form?

If you see, the vector form is very simple. Right, now let's say I have a charge here and a charge here. Let me say this is Q1 and this is Q2. Now, this charge can give a force over this. This charge can give a force over this.

Because it is similar charge, there is a Represive force. So this gives a force on this and this gives a force on this. So how I can represent the coulomb's line in vector form is, let me say F1,2 is force on 1 due to 2. Who gives the first charge? He gives it. So force on 1 due to 2. So K times Q1, Q2 by R.

R is distance. R square. Where does it come from? Electric field.

Who gives the force on this charge? It comes from here. So R21. Right? R21.

So here R cap R21. Very simple. When we say F21, F21 means force on charge 2 due to 1. Where does it come from?

This charge comes from here and this comes from here. 1 to 2. So how I can write K times Q1 Q2 by R square. What is it? Where does it come from? It comes from 1. So R cap 1 2. Very simply our vector form is solved.

This is possible only if there are two charges in the coolums. Now I have multiple charges. So what I can do in that place is, I can go with the Superposition Principle.

So here comes Superposition Principle. So, super positive principle says that I have multiple charges. I don't have two charges. So, if I have multiple charges, it is like this. So, when we have multiple charges like this, we can consider this charge and say what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, what force is given by this, we just add.

So, this one charge, let me say this is Q2, Q3, Q4, Q5, Q6 and Q7. So, let me say that is Q1. So, how can I say, how I can represent my force? What force?

which is equal to K times Q1 and Q2 the distance between them is 1 to square the distance between these two charges so this is 1 to square. When we say 1 and 6 I have 1 and 6 here. So that is K times Q1 Q6 divided by R square that is the distance between 1 and 6 So this is how we find the force of each kind of charge Then we just add F total When we say F total, I get K common everywhere and Q1 is also common so K is common, Q1 is common what we are adding?

summation of QI that is 123456 that is what we are adding so that is I can say that this is from 2 to I similarly we have distance this distance also changes so charge from 1 to n number of charges so you can also say I square so this is multiple charges this is the way I can find my total electrostatic force so next to that this coulomb force and multiple charges we have electric field electric field is another important concept we have to see here so electric field so basically what we know I will sum up all these and finish here so electric field is given or it is coming out from or getting in from negative and positive positive charges so positive charges so the electric field is ready output negative charges so the radio input then the charge will be pocket alert so we have a attractive force which is due to the electric field which is present on this particular charges so either another than I come to the repulsive force over to the attractive force of your copy the momentum so how we can represent in mathematical expression of the party which is equal to F by Q I mean so so for acting per unit charge if I don't want the source charge every now and then the point point charge and the point charge right in the point charge in the electric field I just go with the point charge so in the point charge test charge we always go with the positive charge because in order to find their effect so how the effect is we always go with the point charge and test charge right so we use test charge to test the charge very simple So, there is an electric field. So, when the electric field acts at this point, how much force can be given to this? That is what we call electric field. Electric field is the force per unit charge.

Similarly, when we say positive, the electric field of this also will be affected by this. But, the amount of charge value of this electric field which is not there, is almost 10 to 0. That is what we have said in our book as limit and Q 10 to 0 F by Q which is nothing but electric field. So, this is the meaning of this.

The meaning is, to prevent the electric field from coming from the test charge, if we take this value as 0, the effect of this will affect it completely. To indicate this, they have mentioned this. But also we can also rewrite this as kQ by R square.

Because when we say electrostatic force, it is the force between the two charges. So Q1 and Q2 by R square, by this Q, one Q and this Q will get cancelled. Which is nothing but kQ by R square.

So in the other term, I'm... The important thing to note is that we have not considered the test charge. That is what we have cancelled. Without considering the test charge, we have taken the source charge only.

So, F which is equal to, sorry, K which is equal to KQ by R squared. Very simple. So, what is this? There are two charges.

Suppose, here I have multiple charges. Right, multiple charges. So, this is similar to... That superposition principle.

So, when we say first, what we found? F total which is equal to kq, which we have summed up and divided by 1 i square divided by 1 i square and from 2 we have i. force superposition principle here electric field is same as E total which is equal to same way I have found electric field in two charge fields then we add so in this K is the only common nothing else is common and also source charge is also common source charge is also common so what will change for me distance will change so from 1 to I distance will change so summation So that's all we are going to talk about electric field. And similarly, we will be given another basic understanding part of electric field. So this is positive charge and this is negative charge.

So electric field is all radially outward. To understand this, my strength will be higher near this charge. the distance will decrease as we go that is what we call electric field which is equal to kQ by R square when the distance increases the electric field strength will decrease we can easily understand this here similarly as the distance increases area for 3 electric field line also increases.

So in this way, I have these three electric fields. When the same distance increases, see how big the same three electric fields are. So I can also say that my strength strength is directly proportional to distance and the same distance is directly proportional to area. So area is directly proportional to distance.

So this is a basic understanding. Next we have dipole. Dipole is not a concept.

for that we have electric flux electric flux so electric flux up into the electric for the number of right number of electric field line crossing in a given area electric field line goes and that defines my strength. So, how do we define electric flux? Electric flux which is equal to E ds cos theta.

So, when my angle is 0 degree, it will be maximum. And when my angle is 90 degree, it will be minimum. Why? Because when my area vector and electric field are 0 degree, my flux becomes maximum.

When my area vector and electric field are 90 degree, this becomes minimum. So, this is the reason why we call it electric flux. we will use this concept after that we have another concept dipole, when we say dipole we have equal charges, the charge magnitude will be same direction will be opposite electric dipole two polarities two polarities, one is positive and the other is negative distance at the company now in the midpoint learning the inner echo idea the in gear right up easy a up in a easy a bina in a total distance in the core to a up in a record and I the mother in a dipole moment direction patina negative to positive right dipole moment or the direction patina negative to positive so la electric field a direction patina positive to positive to negative so electric field a direction positive negative dipole moment a direction negative positive so in the dipole the net charge you have to remember always so net charge of dipole that is equal to zero net right net charge total charge because this is also plus this is also minus both are same now 5c is also 5c this is plus 5c this is minus 5c so total net charge in a given dipole when we talk about this the value always becomes zero because both are same we add it will be zero net charge additivity of charges right So this is a small understanding. So in this we have given another case.

What are the cases? In this itself we have given an Axial case. Next we have Equatorial cases. So here I have a positive charge, here I have a negative charge.

The distance to be put in this is a. So the total distance is 2a. Now I am choosing a point.

The distance to this point and this midpoint is R. Now what I am going to do is, at this point. What electric field can be given by these two charges? So we know what electric field is. So far we have learnt electric field which is equal to force per unit charge or kq by r square.

When I get positive charge, my distance from here to here is only this. So my distance is this a, this is r, so I don't need a. So the distance of this is r minus a. Correct?

So, this distance, this charge, this is R and this is A. So, this is R plus A. Correct? R plus A.

So, this is very simple. So, what we are going to do? If it is a positive charge, what I am going to write is KQ by R.

R is the distance between the positive charge and the positive charge. So, R minus A is the whole square. Right, so this is positive charge.

Now, when I say negative charge, it is kq by r square. Here, k, q is negative charge, so minus, right, so minus by distance. This distance is r plus a.

r plus a is the whole square. Right, now what I have done is, I have found out two electric fields. What I am going to do, I am going to just, I am going to total it. So, when I total, what will come?

E total which is equal to, do I have kq in these two places commonly? So, KQ is 1 by R minus A the whole square. Right, R minus A the whole square. This minus is there. So, minus R plus A the whole square.

Correct? Now, what I am doing is, just crossing it. So, KQ.

If this is different, just expand A plus B the whole square for a while. R square plus A square plus 2AR minus F. If this is different, R square will come.

Since there is a minus here, minus R square. a squared will be plus, because of taking a minus here, it is a squared. minus 2ar will be there, because of taking a minus here, it is plus 2ar. whole divided by r squared minus a squared, the whole squared.

In this point, we have a very simple understanding. This plus and this plus, this minus and this minus will be cancelled. So the remaining term is k cube, what is this?

4ar divided by, my a is r squared minus a squared, the whole squared. Since my r is bigger than a, I neglect the a and take only r. Right, I neglect the a and take only r.

If I take only r, it will be 4 to the power of r. The r here and the r here will be cube. So this is nothing but 2 into 2. So what can we do?

2. 2aq is dipole moment. So what we can do is, there is a 2 here, dipole moment is k by r cube. Okay, so this is the basic understanding.

So we have already told dipole moment here, so 2aq is dipole moment. So next we move to equatorial concept. So equatorial concept is a simpler understanding.

Right, so Equatorial. So Equatorial means I have two dipoles. The distance between the two dipoles is A.

The total distance between these two is 2A. So I am going to choose my point in the bisecting point. When I say Equatorial, I mean the midpoint.

point from both the charges. So let me say this is the distance, this is the charge, this is the point, this distance and this distance are the same. So this is positive and this is positive, so this is the force impulse.

this is negative and this is positive so the force is like this so the resultant force is here and here so we have two different components, one sign and one sign both are opposite so it is cancelled, we have one cos theta so this has one cos theta and this has one cos theta so there is a cos theta in plus charge and a cos theta in minus charge so what we are going to find is the total electric field so I need every electric field if we have to pay attention here, I have said that I will measure this distance he is checking the distance I need Right, so E is the force per unit charge or kq by r square. So, r is the distance between the two charges. So, we know the value of k, and the value of q is the charge, obviously, positive charge. R is the distance between the test charge and this.

So, if this is right angle triangle, this is opposite, this is adjacent, and this is hypotenuse. So, when I say hypotenuse, I can also say that hypotenuse square which is equal to opposite square plus adjacent square. Now, please do that again.

distance hypotenuse square than a square than a upon just writing R square plus yes they're almost implementers right number simple move square the head hypotenuse square the square now other than a bridge so you know negative charges alone will either work with you in the changes are today which is equal to K negative charge divided by R square plus a square yeah you know you know you know you know you know you know you know you know you know you know you know you are in you so same of being another I'll be having the same thing again our caner cast it are copying here in the corner cost it a no you give her a cost it a no right if I don't know I'm going to add it up a total which is equal to render the limit here Q okay up around the R square plus a square okay I think I'm going to do a cost it over okay up a how I can write I can write this as 2 times KQ So, cos theta is opposite by hypotenuse. Right? So, opposite by, sorry, adjacent by hypotenuse.

So, cos theta, which is equal to, right, this is the angle, adjacent A by hypotenuse. Hypotenuse is not hypotenuse square. Hypotenuse. This is hypotenuse square. So, root over comes.

So, R square plus A square. Root comes and 1 by 2 is written. I wrote one by one.

So we will substitute this value here. Which is equal to 2 times kq by r square plus a square. Here it is a divided by r square plus a square.

1 by 2. So this is 2 or same. This is 1 by 2. Which is 3 by 2. Now if I write like this. 2 aq is p. k.

There is a negative sign. Don't forget. And here r square plus a square.

3 by 2. Similarly, my r distance is very big when compared to a. So, if we neglect a, what we have r square into 3 by 2. If 2 is big, then it is just r cube. So, Pk by r cube. I get negative here. Why I get negative?

Because my dipole moment and electric field direction are opposite. So, my dipole moment is negative to positive. This is how dipole moment is. Electric field is like this. Both are opposite.

We are just mentioning this as negative. that point has a mark, so make sure that you are mentioning that also right, so this is also done for us so what are we going to do after this? right, so the next concept we have is Axial Equatorial and after that just seeing the topic, we should know right? next we have a Dipole right, so dipole in an electric field What will happen when we place the dipole in electric field?

When we place the dipole in electric field, a very simple thing will happen. So, I have positive and this is negative. The distance to this is a and the total distance to this is 2a.

So, if I place it in... electric field. Right, if you see here, the electric field is like this. So this is positive. Obviously, what is this for me?

This is positive for me and this is negative for me. Both are like this. Both are in opposite directions.

My net force is zero. This is a very important point. net force on the another zero on our neck in the little in a rotating effect on the neck rotating effect on the get possible up in the other we are just a mentioning dark right so dark which is equal to force into distance so your force in electric field in the charger so we know that electric field up into the force per unit charge up of force up into the end the cube to produce a Q times e up a Q times either in over here first so distance between the diaper which is nothing but 2a and this is my maximum and my dipole is like this and my electric field is like this so it is 90 degree so just write sin theta or you can also say 2aq is nothing but p right or pe sin theta or you can also write p cross e in vector form very simple so this is when it is 90 degree 0 degree is minimum 180 degree is minimum, that is, parallel to the dipole moment of electric field is minimum.

Anti parallel, that is, 180 degree is also minimum. When is this possible? When there is a uniform electric field.

The next concept is about continuous charge distributions. Continuous charge distributions. We can also go with three important terms.

So one of them is linear charge density, lambda. the Q by L other the straight wire of the density of the charge of the either solo or you can also say Q which is equal to lambda L even the surface charge density other most sigma and solo Q by a or you can also say Q updated on the here depends on so a Sigma Sigma if it is a volume you can also say Q by volume or you can say Q which is equal to rho V is a little bit So this is linear, this is area, surface area, this is volume charge, density. So this is it.

So the concept we have is based on this in Gauss law. So what I am saying in Gauss law is, So, in gas electric flux is equal to EDS. Right? EDS is cos theta.

So, here I have a sphere and this sphere is positively charged. So, what happens is, there is a charge inside this and this is how the electric field is. Because the... So, the area vector of each surface will be like this.

The area vector of each point will be like this. Right? So, the area vector of each point will be like this.

The electric field will be like this. Right? Each and every point of the area vector and electric field will be in the same direction. Which makes the angle to be zero. So, if I do that, cos theta, cos zero degree is equal to one.

So, EDS. So, flux is equal to EDS. Right, E ds is what we can say.

And also we know that electric field is KQ by R square. ds is the area. This is the sphere, or surface area, which is nothing but 4 pi R square.

If it has radius R. So what I am going to do here is, I am just substituting K, what is the value? 1 by 4 pi. epsilon naught, I have this q, this r square, this 4, this pi and this r square. and there is epsilon only.

So electric flux which is equal to Q by epsilon naught. This charge should be inside the closed surface. These are the important conditions mentioned in Gauss.

We can write it like this. So followed by that, we have 3 kinds of applications. One is a straight wire.

There is a straight wire. In that straight wire, how my electric field will be. We are going to use that by using gas lava.

This is the wire. This wire is full of positive charge. So how will the electric field come out?

It will come out like this. The electric field will come out like this. Now I have to find the electric field in this.

All these are continuous charge distribution. So discrete means isolated charges. Multiple charges, coulomb, forces, superpowers, principle, all these are isolated. Like discrete charges. I don't have discrete charges in nature.

All these are continuous charge alignment. So this straight wire has n number of charges. And the directions of the electric field are positively or negatively outward.

Now what I am going to do is, I am just going to imagine a circular thing. Right, so what I am going to do is, I am going to choose a point and the point will be like this. distance is order a the number of points and I'm making this as a closed one right is there a closed cylinder as important right up in the earth in a party now he put in the in the bottom surface is the bottom is the area vector the surface in the middle of the day you can also able to understand the electric field of the degree so flux of EDS cos theta, EDS cos 90 degree, cos 90 degree becomes 0, the whole term becomes 0. And here also 90 degree, here also whole term becomes 0. So where is this curved surface? So curved surface, since it is a cylinder, my area is 2 pi R L. So we have electric flux which is equal to EDS, gas is Q by epsilon naught.

Very simple. So for me this E, we need to find electric field which is equal to Q by epsilon not DS so Q by epsilon not since it is a linear charge density the Q what I am going to do is since it is a linear charge density straight to wire so in that place we said Q is equal to lambda L so I said lambda L because it is cylinder what I am saying is its area 2 pi R L L is gone so my remaining term electric field is lambda by 2 pi epsilon not up Very simple. So the next concept is a plane sheet. How will I have an electric field in a plane sheet? So like this we have a plane sheet.

In the plane sheet, what I am going to do is, I am choosing a small area. So, I am choosing a small area like that and just writing it. So, I am choosing an area like this on both the sides. We need a very detailed explanation. We have posted a video.

also refer that so in the fast recap and I'm just going in so in the other part in the in the over at the limit open area vector go in the area of the record in the area of the record in the area of the computer since it is a positively charged sheet of the eternal a lot of an ing in the area like the electric field a lot of beer electric field a lot of beer correct electric field Allah you put it opening and a lot of a thing in the la service with the underneath the community degrees economic front to back all 90 degree. Where is it? This is 0 degree for me.

This is 0 degree for me. So what happens here is that only in these two surfaces, the maximum flux is there. So how I can say electric flux which is equal to Q by epsilon naught, similarly EDS cos theta.

So if you see here, in both the places cos theta is 0 degree, but to EDS or E area. So, we have to do ds. There is nothing wrong with that.

And then we have a Q by epsilon naught. Since it is a surface, right, since it is a surface, I am just writing. See what I am saying? See what I am saying? I have E like this, right?

I will bring 2A here. So, Q by epsilon naught, I have brought 2A here. I have brought 2a only. Since this q is surface charge density, sigma a divided by epsilon 0 2 times a a a is cancelled. So my electric field is nothing but sigma by 2 epsilon 0. This was a plain sheet.

Now I want a spherical shell. I have a shell. So, when I say spherical shell, it means how my electric field will be.

So, I have a shell like this. What we are going to do is, we have placed the charges inside. So, the charges will be distributed on the surface. There will be no changes in that. Now I am going to choose a surface in the outer side.

So I have this charge inside the imaginary surface. So we can able to do. So this is capital R and the distance of this is small r.

The distance of the surface. So electric flux is... Q epsilon not I'll be putting a EDS later so since it is a surface charge density you can also mention that s Sigma a by epsilon which is equal to E of in the electric field even a patina sphere surface star so I can also rewrite that as for PE no more in the surface of the circle I'm in the surface of the circle I'm going through the surfaces Liam so you must really This is the charge which we have taken as an imaginary which is nothing but 4 pi r square.

So you can also rewrite this as electric field which is equal to sigma A divided by epsilon naught 4 pi r square. You can also substitute the value of A, sphere, that one becomes 4 pi capital r square divided by epsilon naught 4 pi r square. the 4.4.4 so you have Sigma R square epsilon and R square so capital by small so it will correct the the outside inside the shell so I'm gonna go on slide I saw the inside charge here in the mountain surface in the surface choose funding of the collection of it is applicable of the new the gossel so better even okay in the green color than a choose for the kudi and the imaginary surface and I like a charging occur really and the surface of the object lyric okay up it is not possible I'll be getting What can I say? My electric field becomes zero.

Suppose if I choose this surface, the value becomes this. Right? Then this R will be replaced by R squared, the distance. If it is on the surface. So, don't worry.

I hope there are no doubts. So, we will try to do all the chapters as fast as possible. Thank you. Help others with a smile.

Share this with your friends. Thank you.

Transcript for:Understanding Electric Charges and Fields

Transcript for:
Understanding Electric Charges and Fields