# Electric Field/Gauss' law of cylinder and shell

#### ultrapowerpie

1. Homework Statement
http://img244.imageshack.us/my.php?image=a1physicsmt8.png

2. Homework Equations
Gauss' Law

3. The Attempt at a Solution
It may be that I'm sick with a cold and can't think straight, but I"m not seeing any way to approach this problem using Gauss' law. I tried using a few prederived formulas, but like for the first part of this 5 part problem, I need the charge/length in order to find out E. I don't have that value, and I did try using rho as lambda, and got it wrong. I also have to find the charge at values inbetween the cylinder and the shell, outside the shell, and on the inner shell.

Some help would be nice, as I can't see how to do this by hand right now.

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#### americanforest

Consider a Gaussian cylinder with radius of 2 cm. This cylinder is within the green cylindrical charge distribution. Gauss's Law is

$$\oint_{S}\vec{E}\cdot\vec{dA}=\frac{1}{\epsilon_{0}}\int_{V}\rho dV$$

Use cylindrical coordinates, the given charge density, and the fact that the electric field is parallel to your Gaussian surface's normal vector to solve this.

Note that S is the surface area of your Gaussian cylinder and V is the volume within it.

#### chrisk

Using a cylindrical Gaussian surface will give E in terms of charge/unit length. So, let the Gaussian surface be

$$2\pi\mbox{rl}$$

where l is a unit length. Then the charged enclosed per unit length within this surface is the volume within the surface times the charge density for r less than the radius of the inner conductor.

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