00:01
Let's say that we had a solid conducting sphere within a hollow conducting sphere.
00:09
And we know that the inner sphere has a charge cue on it, but no other charges are placed on the outer sphere, purposefully anyway.
00:20
And the question is, what does the electric field do in the different regions? and there are a few things that we need to work this out.
00:31
One is gauss's law that relates the electric flux through a surface area closed to the enclosed charge, basically saying that the electric field busts out of a charge.
00:54
And you almost never do the integral on the left.
00:59
Left -hand side, and often you don't need to integrate the right -hand side either.
01:05
But we'll also need to understand that in electrostatics, there are some things about conductors.
01:13
And one of those is that in electrostatics, there is no electric field inside a conductor.
01:29
There's a good reason for that.
01:30
Remember that conductors let charges move freely throughout them.
01:37
If there was an electric field inside, the charges would be trying to move around to get as far away from each other as possible, and they should reach that edge pretty quickly.
01:54
And so there's a corollary to that, corollary to that, which is that in a conductor, charges reside on the surface.
02:12
So they're trying to get as far away as possible as they can from each other.
02:18
And that's a place they can go to get far away.
02:22
Then there's no further if there's no more conductor.
02:28
And one result of the charges on the surface is that the e -field is discontinuous, the normal component to the e is discontinuous on the surface of a conductor, which is an interesting phenomenon.
02:56
In any event, what we know for sure in this particular situation is in the two regions of the conductor, the electric field is zero, both with our r is less than b.
03:14
Sorry, less than c, but greater than b, and also when r is less than a.
03:21
So inside the conductor itself.
03:28
And if we drew a gaussian surface, so galses law enables you to imagine a surface, and i'll draw that in red, it's an imaginary surface that you get to think through the electric field on, if i draw a surface, on the inside of that blue shell, the electric field has to be zero, which means that the enclosed charge also has to be zero.
04:05
Okay.
04:06
And the way that happens, you may ask, is, well, gosh, there's a positive charge in there.
04:13
Well, this is where the conductor comes into play.
04:17
The conductor is neutral, but it can certainly charge separate.
04:22
So what will happen is that positive charge will induce an equal but opposite negative charge on the inner surface.
04:35
And that means on the outer surface to remain neutral, the outer surface has to acquire a plus q.
04:50
All right, so if we look at that red gaussian surface then, there's no enclosed charge.
05:11
So where is there an enclosed charge? if we draw a gaussian surface on the hollow, and we'll call that surface one, surface two, and we'll draw another one outside and call that three.
05:34
Now, that's supposed to be a sphere.
05:37
I know i'm starting to get a little sloppy with his drawing.
05:41
But in region one, where r is in between, that surface has a surface area of 4 pi r squared, and the enclosed charge is plus q.
06:05
And so we can find the electric field in that region.
06:15
It just looks like 8 point charge.
06:17
And you may be familiar with that, at a sphere.
06:23
Symmetric sphere.
06:25
By and large, its electric field is the same as a point charge concentrated at the center.
06:35
And again, if we look at region 3, which is not inside any blue stuff, we still have er.
06:46
Whoops...