Infinitely Long Cylindrical Surface Problem

[jordanjj]

Homework Statement

Here is my problem. I don't fully understand Gauss' law so any assistance there would be greatly appreciated
Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 4.00×10-2 m. The charge density is 1.00×10-2 C/ m3. What is the electric field at r = 2.00×10-2 m?
(in N/C)

Homework Equations

The Attempt at a Solution

I understand that gauss' law is the integral EdA and that the E for a cylinder is lamda/2pi(E0)r , but I don't understand it for an infinite cylinder

 

[jordanjj]

nevermind figured it out

 

[Delphi51]

You mention Gauss' law, so maybe you are supposed to use it to find the answer rather than that formula. You must imagine a cylinder that has the point you are interested in on its surface. Just the given charged cylinder will do nicely in this case. You figure out how much charge is inside - maybe use L for the length and let it tend to infinity in your final answer (most likely it will cancel out before then). Looks like E will be the same at all points around the cylinder so that integral is very easy. Solve for E. I would expect the answer to be just that formula lamda/2pi(E0)r which is for an infinitely long line of charge.

Of course you will put the numbers into find a numerical answer.