00:01
Let's say we have a sphere here that has a total charge q -0, and let's say it has a radius of r, and we want to find the electric field both inside and outside the sphere.
00:14
So the electric field outside the sphere is actually quite easy, because we can use gauces law to do this.
00:19
So this says the closed loop integral of e over the surface, we'll call it d .s, is equal to the total charge and closed, which we know is going to be q -0 over epsilon -0.
00:30
Let's just call this q to make things a little bit, i don't know, more familiar.
00:35
So the electric field is radially symmetric because the volume charge density is symmetric.
00:42
And so what that means is we have e times the surface area of the sphere, because the electric field is constant at every point is equal to this, q over epsilon not.
00:52
And so that means our electric field outside the sphere is the familiar result from kulam's law.
00:59
So we could write this as 1 over 4 pi epsilon not times q over r squared.
01:06
So that's our field outside the sphere.
01:09
Inside the sphere, let's let the charge inside the sphere, the charge enclosed by our gaussian surface...