# Calculate Electric Field and Magnetic Field

1. Apr 11, 2010

### noamsgl

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

Given a long cylinder with radius R, is charged with a homogeneous charge density ρ and is rotating with frequency w around it's symmetry axis.

A. Find the Electric Field E in every point in space.
B. Find the Magnetic Field B in the cylinder with distance r from the axis of symmetry (r<R)

ρ,w,R ------> E=?, B=?

2. Relevant equations

Angular Velocity = w*r
[PLAIN]https://www.physicsforums.com/latex_images/25/2542612-8.png [Broken]

Some equations with charge density and velocity... I=J*L or something.

3. The attempt at a solution

I am clueless about the answer to A and the Electric field, although I am sure it is more of a logic problem than some long equation/calculation. I'm just not sure what to write though.

I have tried and am optimistic about my approach to B and the Magnetic field.
I might be totally off-track but this is what I tried.
I guessed that this problem is analogous to many many long coils stacked inside one-another, and that I want to find the current as a function of a small radius r (r<R).

I wanted to find the electric current I(r) and then plug it into Ampere's law, what I got so far is this:

dI= J*L*dr = ρvL*dr=ρ*w*r*L*dr

Now I need to integrate all these little 'dI's from r to R (right?).
So I tried it and this is where I think I made a mistake.

Ienc = /int[r][R] ρ*w*L*r*dr = ρ*w*L*pi*r2

Then I took that and plugged it into Ampere's law, but apparently my answer is incorrect.

Thanks a ton to whoever spends the time helping me. Please help me understand why this is incorrect and not just provide an answer, and also give me some tips on the Electric field. Many thanks.

Last edited by a moderator: May 4, 2017