00:01
Let's talk about this question.
00:02
We are given that a metal sphere radius r1 has a charge of q1 and we have to take the negative potential to be zero at infinite distance from the sphere.
00:10
Part a talks about what is the electric field and the electric potential of the surface of this sphere? so if this is a sphere having a charge of q1 and this is a metal sphere, so definitely everything will be on the surface, that's the property of the metal.
00:25
If we talk about the electric potential or the electric field, that anywhere on the surface then this charge actually a sphere actually behaves like a point charge have at a distance of r1 from that point so we know that if we talk about the electric potential that's going to be q1 over four pi aps knot r1 and this can be written as kq1 over r1 so this is the required potential and if we talk about the electric field that's going to be q1 over 4 pi abs not r1 square so that's going to be can be written as kq1 over r1 square so that is the required electric potential there's a required of there's a required electric field and electric potential at the surface now this fear the sphere is now connected by a long thin conducting wire to another sphere of radius r2 and there is several meters from the first sphere so there's a reason why they are seeing that it is several meters from the first sphere i will talk about it in a before the connection is made the second sphere is uncharged so let's let's see how this looks like so we have uh this as the first sphere uh with q1 and r1 and this is the thin cable with which we are connecting another sphere of some unknown charge q and radius r2 now after the lactrostatic equilibrium has reached what are the total charges uh on each sphere all right so uh since they are connected with the conducting a wire it means that the charge will flow from q1 to the other uncharged sphere q this is uncharged i'm really sorry there's no q here uh q such that they're both potential remains the same now the point is over to q1 the potential is definitely due to q1 and due to this sphere but uh since they have said that they that they that is several meters from the first sphere, which means that we can ignore the effect of this charge over here and vice versa of this charge over here.
02:42
So at this surface, the only potential is created by the charge q1 and the same is applicable for the other sphere as well.
02:51
So let's say the x charge moves from here to here.
02:54
So the new charge on it, that's going to be q1 minus x and the charge on this is going to be x and it was on charge initially.
03:00
So this happens until when their potential becomes same.
03:04
So kq1 minus x over r1 must be equal to kx over r2.
03:11
So k is canceled.
03:14
This is a proportion.
03:15
Let's do a cross multiplication here.
03:17
We have q1 minus x times r2 is going to be equal to x times r1.
03:23
Let's open up the parentheses here.
03:25
So we have q1r2 minus r2 x is equal to x r1.
03:30
Bring this one over to the right.
03:32
So we have q1r2 is equal to x is taken as a common factor.
03:37
We have r1 plus r2 and the final value of x comes out as dividing both sides by r1r2.
03:43
We get q1r2 over r1 plus r2.
03:46
So this is the charge which is flown from the surface 1 to the surface 2...