# Homework Help: Electric field calculation

1. Oct 24, 2009

### edwiddy

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

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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.

EDIT: issues with tex.

2. Oct 24, 2009

### 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:

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

3. Oct 24, 2009

### edwiddy

Gotcha gotcha, seems so obvious in hindsight, thanks.