A solid conducting sphere carrying charge q has radius a it...

A solid conducting sphere carrying charge $q$ has radius $a$. It is inside a concentric hollow conducting sphere with inner radius $b$ and outer radius $c$. The hollow sphere has no net charge. (a) Derive expressions for the electricfield magnitude in terms of the distance $r$ from the center for the regions $r < a, a < r < b, b < r < c$, and $r > c$. (b) Graph the magnitude of the electric field as a function of $r$ from $r =$ 0 to $r =$ 2c. (c) What is the charge on the inner surface of the hollow sphere? (d) On the outer surface? (e) Represent the charge of the small sphere by four plus signs. Sketch the field lines of the system within a spherical volume of radius 2$c$.

Transcript

00:01 Let's say we have a red conducting sphere as you can see in the diagram there in the middle as a radius of a.

00:08 In a charge of plus q.

00:11 And that red conducting sphere is surrounded by empty space, but it's also inside of a larger green conducting sphere.

00:19 Right? and this fear is hollow.

00:22 So it has an inner radius of b.

00:24 And an outer radius of c.

00:27 Um and this outer sphere, like the green one, there has no charge on it, no net charge.

00:33 So let's find the electric field at a few different points.

00:36 And and to do this, we're gonna be using what's called god's law, right? and god's law for electric fields basically says that the integral of the electric field in terms of the area d.

00:53 A.

00:54 Is equal to the charge enclosed.

00:57 So q.

00:58 E.

00:58 N.

00:59 C.

01:01 I'm trouble getting to see there right over the constant e.

01:05 Not right.

01:07 Which is the primitive itty of free space.

01:09 So the first thing to know is that the electric field inside of any conductor is always zero.

01:19 So that means we don't even need god's law for inside the red conductor.

01:24 This is just going to be zero.