Charged coaxial cable - Charge distribution?

[quanticism]

Homework Statement

Say we have an infinitely long wire with radius r1 with a linear charge density +u and we have a coaxial conducting cylinder with radius r2->r3 and a linear charge density of +2u.

http://img573.imageshack.us/img573/3419/coaxialcable.png"

Now the overall aim of the question is to find the electric field at various points away from the centre.

ie. r<r1, r1<r<r2, r2<r<r3, r>3

2. The attempt at a solution

But before I can do that, I need to know how the charges are distributed in the two conductors.

Now we know that a conductor in electrostatic equilibrium has these properties:

1) The electric field is zero everywhere inside the conductor (whether hollow or solid)

2)If the conductor is isolated and carries a charge, the charge resides on the surface.

I can't seem to visualise how the charges will distribute. My initial impression was that it would do something like this but now I'm not too sure.

http://img221.imageshack.us/img221/3233/chargedistribution.png"

Any nudges in the right direction would be nice.

 

[quanticism]

I think I understand how the charges distribute now.

The central wire must have the net charge distributed on the outer surface (at r=r1). So the linear charge density along this surface is +u.

The inner surface of the conducting cylinder (r=r2) must have a linear charge distribution of -u. This is to ensure that the electric field from r2->r3 is zero (shown using Gauss's Law).

The question said the conducting cylinder had a linear charge density of +2u so that means the outer surface of the cylinder (r=r3) has a linear charge density of +3u.

Is this correct?

 

[ehild]

Yes.

ehild