 Okay, so let us start this topic gravitation potential. It is not a school level topic, okay? So we are, we've already done the school level thing, okay, gravitation long back. We are moving ahead from the school level and we are discussing the some advanced topics, okay? Like for example, last class towards the end for about an hour, we had a discussion on gravitational field, okay? Fine, so gravitational field we discussed. What is the gravitational field? It is force per unit mass, okay? So if you have a gravitational field given, you can find the force by just multiplying mass with that gravitational field, all right? So we have the formula for the force between two point masses or two spherical masses, okay? But when it comes to different kind of structure, we need to actually integrate and find out, all right? So that is why we have defined something called gravitational field. So that we find field with respect to different, different kinds of shapes and sizes, which are regular shapes and sizes. And once you find the field, then if you put a point mass over there, then the field multiplied by the mass of that point mass will be the force, okay? So the gravitational field is a useful concept, all right? So now you should be comfortable with respect to that, but then we have not discussed the situation where two bigger masses are there. For example, one ring is there, another disk is there, okay? That is a very complicated scenario that is actually not in J advance syllabus also, but that we may take it up in class 12 later on, but not now. What we have done is we have found out the force between two point masses and we have found the force between one bigger mass, which could be ring, disk, sphere, or whatever shape and size could be a wire, one bigger mass and a point mass. We haven't considered the situation of one bigger mass and another bigger mass, fine? Now, in this particular section, gravitational potential, we are going to introduce another physical concept, okay? So I'll just talk about the need of this, why there's a need of this concept. Good to see that attendance is around 17, 18, even though tomorrow is max, nice to see that. I hope you'll be there till the very end of the class. Now anyway, I know who all are there in the class. Okay, so suppose you have two masses, okay? Two point masses are there, M1 and M2, they're separated by a distance of R, okay? Okay, the potential energy between the two masses or the system, the potential energy is what? Minus of G, M1, M2 by R. This is the potential energy, okay? The issue with this particular formula for potential energy is that it requires the presence of both the masses, fine? All right, so only if M2 is there, okay? Only M2 is there, then there is no potential energy, potential energy is zero, okay? And if you put a mass M1 over here, suddenly potential energy appears, okay? So there must be something over here because of only M1, because of only M1, due to that only the potential energy is coming, fine? So we are going to find out what is the effect of M1 at the location of M2 because of which potential energy is coming in, all right? Because only if M2 is there, there is no potential energy. Suddenly you keep M1 and potential energy appears, okay? So we are in search for a function which could represent the energy and it is only a function of M1, okay? So what we do, we already have a formula for potential energy. We say that potential energy per unit mass at that location, this particular thing is a function of only M1, okay? So I can say that potential energy could be because of M1, M2, but potential energy per unit mass, that is only a function of that mass M1, okay? So it is good to have this expression, okay? Because if you multiply this particular expression with whatever mass you keep here, you will automatically find the potential energy, okay? Just like if you multiply mass with the field, you get the force. Similarly, if you multiply this particular expression with the mass, you get potential energy, okay? So the name of this thing is potential. It's not potential energy, fine? So write down potential. So again, I'm telling you, we are going ahead of your school syllabus. We are not restricting ourselves to just schools, okay? So that's the reason why we are taking up a few advanced topics. We are towards the end of this chapter. So just one more R and this chapter will be over. All right, so potential, write down potential due to, due to a point mass at a distance of R from the point mass, due to a distance of R from the point mass is minus of GM. By the way, this potential and field, they are not as such, they are just a concept, okay? So we have just assumed that there are multiple scenarios and we have derived it. In fact, you can treat whatever derivations we have done as if we have solved few numericals, okay? So when you talk about concept, that's it. I could stop here and say that gravitational potential is done, all right? But we, like I'm also assuming different kinds of scenario and keep on doing derivations for them. So there can be endless such situations, fine? So that's what it is. You need to solve a lot of questions your own related to potential and field to get comfortable with these topics, all right? So this is the potential. Can you tell me what is the direction of the potential? Which direction it is? Correct, it's a scalar quantity, okay? It's a scalar quantity. The best part, no direction, right? So whenever you find the potential of anything, you don't have to worry about the components, fine? You don't have to find out the X component, Y component, all that, okay? You just treat it like a number and you just add them up. Getting it, what is the unit of the potential? What could be the unit of the potential? Give me one of the obvious units of the potential, quick. Potential energy is joules, right? Potential energy per unit mass is joules per kg, okay? Any doubts till now? Now we'll be taking up different kinds of scenarios and try to find potential for those. Any doubts till now? Quickly type in, what else? Okay, so we'll be taking up one by one different scenario just like we have taken up with respect to the gravitational field, okay? So if I ask you to do some scenarios, when I ask you answer, then only you type in, okay? So that others are also comfortable solving it, right? So let's do it for ring, for ring of mass M and radius R. What is the potential? All of you, yeah, that's a valid question. You have to ask where, where I have to find the potential? Okay, potential at the center, how much it is? Okay, if anybody got the answer, please type in. Why it is zero? What is the reason for it to be zero? Yeah, it's a scalar. So you can't say that one direction then opposite direction will cancel out. So it cannot be zero. Had it been field, then yes, because of this point mass, let's say you take a small mass over here, the field will be like this, and because of this one, the field will be in opposite direction, so they will cancel out each other because it's a vector. But potential is not a vector, so there is no question of direction, fine. So I think all of you are not getting it. Anyways, so here, tell me, if you take a small mass over here, dn, okay? It's distance is R, yes, they've asked, that is correct. Okay, so the potential due to this dm mass is what minus of g dm by R, right? This is the potential, and the best part is that the distance of all the point masses is capital R, all right? So you can just put the integral dv to get the value of total potential and minus g by R will come out of integral. It'll be simply integral of dm, that is m only. So minus of g into capital M divided by R. So this is the potential due to a ring at the center, okay? Understood all of you, why are you getting wrong, right? Any doubts? Okay, now write down something which is very important that write down if all the mass of a system is at a distance of d, okay? So all the mass of a system of mass, let's say capital M is at a distance of d, then potential or gravitational potential I'm talking about, then the potential v will be simply equal to minus of gm by d, okay? So you don't need to integrate or anything. If you're seeing that all the mass of the entire system is at the same distance, is at the same distance from the point where you're finding the potential, then you just directly write minus gm by d as the potential, fine? Because when you integrate, g by R will come outside, g by d will come outside all the time. It will be simply integral dm, which is m only, okay? So let's take few more scenarios which is similar to this, okay? So another scenario is this one. You have a ring of mass M and radius R, you need to find out the potential along the axis at a distance of d, okay? This is mass M and radius R, okay? This ring is perpendicular to the plane of your screen. That's wrong Bharat. Others, this is where you need to find the potential. Now answer me one thing is all the mass, all the mass of this ring is at the same distance from that point, yes or no? Right? Yes, Sushant. Now it's like a cone, fine? So if you could visualize in 3D, it's like a cone, Bharat negative into negative is positive. So this distance is root over R square plus d square, okay? So all the mass is at a distance of root over R square plus d square only, okay? So the potential in this case is minus of gm divided by root over R square plus d square, understood?