# Homework Help: Derive Electric Field of Cylinder Via Gauss' Law

1. Sep 4, 2010

### Jawbreaker

1. An infinitely long cylinder of radius R contains a uniform charge density Rho. Calculate the electric field using Gauss' law for r> R and R>r

3. I attached a pdf with my attempt at r>R. My answer doesn't agree with those given http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html#c3". I noticed that length canceled but I'm not sure if my set up was done correctly. I solved the same problem using direct integration of Coulombs law and there I took the limit of L as it approached infinity. Any suggestions would be great. Thank you :]
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### gauss.pdf
File size:
340.6 KB
Views:
167
Last edited by a moderator: Apr 25, 2017
2. Sep 5, 2010

### G01

You just dropped the factor of r on the LHS of the second to last line. Other than this algebra error, your answer is correct.

3. Sep 5, 2010

### Jawbreaker

Alright thanks for catching me there. So this is a correct way for setting up a problem for an infinite cylinder? I couldn't wrap my mind around how you could use gauss' law for an infinite surface or volume.

4. Sep 5, 2010