How Do You Calculate the Electric Field Between a Wire and a Cylinder?

[edwiddy]

This is for a stat mech class which randomly has a homework question with an electric field calculation. It's been a while, so I've forgotten a lot :(

Homework Statement

We have a wire of radius $$r_0$$ that is coincident with the axis of a cylinder with radius $$R$$ and length $$L$$. The wire is maintained at positive potential $V$ with respect to the cylinder. Find the electrostatic field that exists at $$r, r_0 < r < R$$.

There is some thermodynamics stuff about the electrons forming a dilute gas, etc, but since we're given no information about the density and stuff I assume that they won't affect the electric field.

Homework Equations

Gauss's law: $$\Phi = \frac{Q}{\epsilon_0}$$
Definition of potential: $$\int_{r_0}^{R} E dr = V$$

The Attempt at a Solution

The issue is pretty straight forward. I plan on picking a cylinder with radius $$r$$ around the wire as the Gaussian surface for Gauss's law. However, I can't seem to use the potential with Gauss's law.

Thanks in advance.

EDIT: issues with tex.

 

[Donaldos]

Let $$\lambda$$ be the linear charge distribution in the wire.

Use Gauss's Law to express the electric field in terms of $$r$$ and $$\lambda$$.

Then use this:

Definition of potential: $$\int_{r_0}^{R} E dr = V$$

to determine the expression of $$\lambda$$ as a function of $$V$$.

 

[edwiddy]

Let $$\lambda$$ be the linear charge distribution in the wire.

Use Gauss's Law to express the electric field in terms of $$r$$ and $$\lambda$$.

Then use this:




to determine the expression of $$\lambda$$ as a function of $$V$$.

Gotcha gotcha, seems so obvious in hindsight, thanks.