# Magnetostatics problem: find B and H

1. Sep 5, 2011

### summerwind

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

A long wire carries a current I and is centered in a long hollow cylinder of inner radius a and outer radius b. The cylinder is made of a linear material with permeability $$\mu$$. Find $$\mathbf{B}$$ and $$\mathbf{H}$$ everywhere.

2. Relevant equations

3. The attempt at a solution

The only free current in the problem is the current in the wire. Therefore, by Ampere's law,

$$\mathbf{H} = \frac{I}{2 \pi\ p}\ \boldsymbol{\hat{\phi}}$$

(I'm using cylindrical coordinates with the wire at p = 0 and the current moving in the +z direction.)

For 0 < p < a and b < p, we have $$\mathbf{B}=\mathbf{H}$$. For a < p < b, we have $$\mathbf{B} = \mu\ \mathbf{H}$$.

If this solution is correct, would anything be changed if I said that the hollow cylinder with permeability $$\mu$$ was also a conductor (made of steel, say)?

2. Sep 6, 2011

### rude man

Your solutions look right to me, but you use the cgs system & I use SI so to that extent I don't know, but as I say they all look right.

The fact that it would be a conductor, e.g. Cu, is of no consequence. Cu is non-magnetic.

But - you said steel - steel has a very high permeability so to that extent your numbers would be quite different inside the steel.