00:01
All right, so let's say we have a disk that has a radius r and is uniformly charged with the surface charge density sigma.
00:07
And we want to evaluate the electric field at the distance x away from it.
00:11
So the electric field on the x axis of a ring is going to be like k times the total charge on the ring times x divided by x squared plus r squared to the three halves.
00:28
So if we write this as a superposition of rings, then we can figure out the electric field here.
00:34
And it's only going to be in the x direction.
00:37
So we'll just look at the x component.
00:38
The y component's going to be zero due to the symmetry of the problem.
00:43
So our infinitesimal electric field here is going to be, of course, kulam's constant times dq times x over x squared plus r squared to the three halves.
00:56
And so what is dq? well, dq is going to be like sigma.
01:01
If we take a little ring here, let me maybe draw a little bit better.
01:08
The charge on that ring is going to be sigma times the 2 pi rdr, and r here is our little distance.
01:20
Sorry, i should have written a little r squared rather than capital r.
01:26
So this is little r...