Gauss Law - Conducting cylindrical shell

[MichaelT]

1. A thick conducting cylindrical shell has an inner radius Rsub1 and outer radius Rsub2. It has a net excess charge = Q, and it is L long. Find electric field at certain points given.

Ok, when r is less than Rsub 1, the electric field is zero. And when r is greater than Rsub2, it is easy to calculate using Gauss's Law. Now, when r is between Rsub1 and Rsub2...what is the excess charge inside the Gaussian cylinder? I know that any net charge in a conductor must be on one of the surfaces. But on which one, and how much on each?

This might be a silly guess, but maybe Q/2 ?

 

[Doc Al]

What's the field within the material of the conducting shell? (Between R_1 and R_2.)

 

[MichaelT]

The electric field inside the material of a conducting shell is zero when the conductor is in electrostatic equilibrium. Does that still hold even though this conductor has a net charge of Q?

 

[Doc Al]

Absolutely.

 

[MichaelT]

Ok, that's cool. A little strange to me though. Intuitively it does make sense, but when you use Gauss's Law, wouldn't there be some excess charge inside a Gaussian cylinder with r between R_1 and R_2? Or would the excess charge Q remain on the outer surface of the conductor?

 

[Doc Al]

The excess charge can only exist on the surface of the conducting cylinder. Since there's no charge contained in the cavity (at r < R_1), there's no charge on the inner surface. (Convince yourself of this using Gauss's law.) Thus all excess charge is on the outer surface.