00:01
All right, so let's say we have a charged distribution in some region of space given by a over r, and presumably this is for some distance within a radius.
00:11
And we want to find the electric field everywhere in space.
00:15
So we'll use gauss's law, and we'll draw a gaussian surface of radius r here.
00:21
And so what we know is e times 4 pi r squared, because we don't have to worry about an integral, because this is spherically symmetric, so it's constant at all radii, at a given radius anyway.
00:34
The charge of distribution is constant.
00:37
This is going to be equal to the total charge enclosed up to that point divided by epsilon knot.
00:42
So what is the total charge enclosed up to a point? this is going to be the integral from 0 to r of row of r prime times 4 pi r prime squared d r prime.
00:57
And so if we write this, this is 4 pi a times the integral from 0 to r, and it's actually pretty simple.
01:04
It's just r prime, dr prime...