 Fine. So shall we start this chapter revision? All of you have come prepared. Yes. Okay. Fine. So we are going to first see what are the concepts in this particular chapter and quickly revisit them. Give me a moment. I will open up a book so that I don't miss anything. Fine. All right. So this chapter has clearly three sections. First one is intro to the charges. Okay. So in this particular section, we are going to discuss about the we have properties of the charges. For example, charges cannot be as in created or destroyed. They are conserved basically in a closed system. Okay. So there are certain properties of charges which are very obvious on the face of it. But when we solve numericals, tricky to apply. So into two charges, then we have another section of the chapter that talks about Coulomb's law. And in this section only introduction of electric field is there. Okay. And then towards the end, we have a very powerful law that is Gauss law. Okay. Gauss law, Gauss theorem, whatever you want to call it. So these are the three chunks. And then when we discuss about the electric field, we will also discuss about dipoles. As in we would have discussed about the dipole as well. All right. So now when it comes to introduction of charges, we have the most important law inside introduction is conservation of charge. Okay. So in a closed system, in a closed system, the total charges conserved. Okay. What does it actually mean is that suppose there are two objects A and B, like this A and B are the two objects and you define your boundary with an image. So you define your system with an imaginary boundary like this. Okay. Then A and B can exchange charge. Okay. They can give charge to each other. And suppose from outside, there is no charge exchange. Then whatever was a charge initially Q1 plus Q2 will be the charge finally Q1 plus Q2. This is the conservation of charge for an isolated system and charges, relivistically invariant also as in kinetic energy depends on your velocity also. When you are running and observing something relative velocity you'll observe. So kinetic energy will be something else. Okay. But charge doesn't depend on relativity. Fine. The charge is relivistically invariant anyways. So this particular section will be talking about the charging also. Charging is done in three different ways. Induction, conduction and friction. Right. So conduction is the next chapter as in the third chapter that talks about current electricity. Induction is random process. So induction is a process which is very important. As in some questions they are solved by proper understanding of induction itself. So what is induction by the way? What it is induction. What does induction mean? How it is done charging without any contact. Induction is usually separation of charge from a neutral object. So if you bring a positive charge near to this metallic sphere, negative charge will get attracted here and positive charge will get attracted there. So if you could exploit the separation of charge to create a net charge, that is where the charging due to induction comes. Fine. Okay. Then comes the Coulomb's law. According to Coulomb, the force between the two charges is this. 1 by 4 pi epsilon naught q1 q2 by r square. Now the way we will be solving questions is that we are not going to take the signs of charges q1 and q2 while using this expression because sign only will indicate the direction of force. So I will not include the sign when I calculate the force. I already know whether it is attractive force or repulsive force. So if it is minus 2 Coulomb, I will take as plus 2 like that. The force is along the line joining the charges. And this is true only for the point charges. If you keep it in a dielectric of dielectric constant K, epsilon naught will become K times epsilon naught, where K is the dielectric constant. Okay. So the force between the two charges will become 1 by K times the earlier force. All right. Now the thing is that sometimes we call 1 by 4 pi epsilon naught itself. We call 1 by 4 pi epsilon naught itself as some constant K whose value is 9 to 10 is for 9 SI units. So what I was saying was that this force will give you expression only for the point charges. Suppose you are dealing with the bigger charges, then you have to define something called electric field. Then only you can deal with the distributed charges or bigger charges like that. So electric field concept is there, which is nothing but in this case, in case of electricity, electrostatics, it is force per unit positive charge. So that is KQ by R square. Now the only difference between this expression and that expression, there are two variables of charge, Q in and Q2. The force depends on both the charges, but electric field depends on only one charge. So it is easier to deal with the electric field because electric field will be due to a single charge, as in what is the effect due to the single charge. So now this effect, I can add it up. I can find out electric field due to let's say a rod which has multiple positive charges. I just keep on adding electric field due to each one of them. So that is why electric field is useful and once you find the electric field and then you put a charge, point charge Q, the force on that point charge Q will be Q into electric field E. And of course electric field is a vector quantity. If you have an infinite wire like this at a distance of R, what is the electric field? What is the electric field over here? 2k lambda. Lambda divided by 2 pi epsilon naught R. This is the electric field. Now if you have a finite wire, suppose you have a finite wire, same thing like magnetism situation. This is theta 1, theta 2 and the perpendicular distance is let's say R, lambda per unit length is the charge. So electric field is how much? Lambda over 4 pi epsilon naught R into sin theta 1 plus sin theta 2. Okay, so you are saying along which direction it is? Sir, it will be along the... There will be two components of the electric field. Electric field along x axis which is like this. Electric field along the y axis like that. There is no symmetry, so they need not cancel out. So E x is lambda divided by 4 pi epsilon naught R sin theta 1 plus sin theta 2. This is E x along x axis. Electric field along y axis is lambda divided by 4 pi epsilon naught R cos theta 1 divided by cos theta 2. So you can see that when we are talking about an infinite wire, theta 1 and theta 2 both will become equal and 90 degrees. So only E x will remain, E y will become 0 and E x will become equal to that. Talking about the electric field, we have also found out for various other cases. For example, for circular ring, what is the electric field at the center? Zero. Okay, others also speak up. You can type your answers. So suppose you have a ring of charge point length lambda and the radius is A. At a distance x along the axis over here, I am trying to find out the electric field. How much it is? At the center it is zero, yes. Type it out. What is the electric field? Okay. So in terms of total charge, you can write first, it is K Q x divided by, looks like you guys did not come prepared. This Q is equal to lambda into 2 pi A. Okay. Anyways, this is for the circular ring for a disc at a distance of x similar scenario. Can you tell me if charge per unit area is sigma along the axis? What is the electric field? No one? So electric field will be along the axis. It will be K sigma 2 pi 1 minus x divided by root over x square plus r square. K is 1 by 4 pi epsilon naught. Okay. See, you may or may not remember this, but if you do not remember it, you may have to derive it. Okay. All right. So then we have Gauss theorem, Gauss law. So according to Gauss law, integral of E dot dA is called Q enclosed by epsilon naught. Now what is this left hand side? What it is? E dot dA. So the flux. Okay. What is flux? Measure of line is magnetic field. Number of field lines per unit area. Yes sir. What is the representation of that? It is per unit area, the flux. No. This flux is number of lines, not density. Total number of lines. Okay. Electric field is lines per unit area. When you multiply electric field area, you get number of lines. And this is flux over an enclosure. This enclosure is a 3D enclosure. It can be imaginary. Okay. So when you are able to integrate this, this integral will be equal to charge enclosed inside that imaginary enclosure divided by epsilon naught. Okay. So this integral is not very easy to find. The problem is everywhere electric field need not be same. Everywhere angle between electric field and area need not be same. Right. So if electric field is not same everywhere along the area, you get multiply electric field on the left hand side when you integrate. So for symmetrical cases, you can exploit symmetry so that on the left hand side, only one electric field is coming in. And then you will be able to use the Gauss law to find the magnitude of the electric field. Okay. So to apply the Gauss theorem, you must know the direction of the field prior only. All right. Gauss law will be used only to find the magnitude. For example, if you have an infinite wire like this, infinite line charge, you take a Gaussian surface like this. Can anyone tell me why we are taking Gaussian surface like cylinder? Why not a sphere? So that it's convenient for us to integrate without a filter. Because the, because we know the direction of electric field is radial and we know on the lateral surface on the lateral surface of the cylinder, electric field will be constant. Magnitude of electric field will be constant. That is the reason why. Now if it is an enclosure, you'll have two surfaces, one up and bottom. So over here, electric field direction is outwards, outwards like that over here, over there also like this. So you can see electric field being like this because of which the angle between electric field and area is 90 degree on the upper surface and on the lower surface. And on the lateral surface, the angle is zero. So when you take this integral, you will have e into 2 pi rl on the left hand side and charge in close is lambda into l divided by epsilon naught. So from here, you can get the value of electric field easily. All right. Similarly, you can use Gauss theorem to find out the electric field due to an infinite sheet of charge. How much it is? Sigma by 2 epsilon. Sigma by 2 epsilon naught is the electric field and it is independent of the distance from the sheet. The assumption is sheet is infinite. All right. It automatically means that you are very close to the sheet itself. Again, I'll summarize here over here. Flux represents number of field lines. Number of field lines is flux and the magnitude of the electric field is the density of the field line. Okay. Fine. Now, there is a small section of the dipole also. All right. Where in we introduce the dipole and find out its electric field, why we are introducing dipole because naturally isolated charges don't exist. But naturally dipoles do exist. For example, exhale molecule is a dipole only. Fine. So first of all, there is a definition of dipole moment as in what it is we have quantified that. So dipole moment is a vector from negative to positive side like this. This is a dipole moment vector represented as P. Okay. And if the distance between the two charges is to a and charges Q the magnitude of dipole moment is to a into Q the distance between the charges into Q. Fine. So the electric field along the axis over here. What it is Kp by Rq at a distance of R over here. Electric field. No, that is not correct. Electric field is Kp by Rq. So along the axis the electric field is in the direction of P direction of dipole moment. Fine. And at a distance of R at the equatorial plane over here. What is the electric field minus Kp by Rq to minus P by Rq. So you can see here it is like a magnetic dipole only or magnetic dipole is like an electric dipole. Instead of K write down mu not by 4 pi. Instead of P you write down the magnetic dipole moment. The formula is same exact same formula is there. So if you remember one the others you can easily remember. Okay. So till now we have been discussing about the what we have been discussing we have been discussing about the effect of the charge what happens if charge is there what happens if a dipole moment is there. Now we will be you know there is one part of the chapter that talks about what happens to the charges in external field what happens to the dipoles in the external field. Okay. So if if charges are dipoles they are kept in external field external electric field the force on the charge is simply Q into E. We are not talking about potential or potential energy today. Okay. That will be taking up in the next class. This is the effect. Then on a dipole what is the force if electric field is uniform? E cross E. Okay. It is 0. 0. It is 0 on a dipole if the electric field is uniform. Okay. Torque is P cross E. Fine. So I guess that's all. This is what the entire chapter we have.