# Gauss' Law: Enclosed Cylinder in a Hollow Shell

1. Sep 21, 2008

### snakeums

A long non-conducting cylinder has a charge density p = a*r, where a = 4.73 C/m^4 and r is in meters, and a radius of 0.0437m . Concentric around it is a hollow metallic cylindrical shell with an inner radius of 0.119m and an outer radius of 0.158m.

1) What is the electric field at 0.172m from the central axis? Answer in units of N/C.
2) What is the surface charge density inside the hollow cylinder? Answer in units of C/m2.

For part 1 I've already solved a few equations for charges at various radiuses along the inside of the cylinder, between the cylinder and the shell, etc, and I have the equation of (a*r^3)/(3*R*ε0), but I know this won't work because the radius is now outside the shell. I know the shell has no net charge, conceptually, so the charge outside is negative... but I'm still not sure what my R is for this equation.

For the second part I'm almost totally lost. The E = ($$/sigma$$)/ε0) doesn't make sense to me unless I'm supposed to get E for the radius JUST inside of the shell and use that.

Last edited: Sep 21, 2008
2. Sep 21, 2008

### Gear300

I'm thinking you're right about the second part, so all you technically need is the electric field. To make things simpler, you could convert the volume charge density to a linear charge density. The metallic shell doesn't devote to the electric field outside of it, so you could rely on the derived equation for outside the shell and near the inner surface of the shell.

3. Sep 21, 2008

### snakeums

Well I tried the second part by using (a*r^3)/(3*R*ε0), where r = 0.0437 and R = 0.119 to get E. Then I multiplied by ε0 again to get the (surface charge density) but I got 0.011056 which was wrong. So I guess I'm more lost than I thought.