(adsbygoogle = window.adsbygoogle || []).push({}); 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 [tex]\mu[/tex]. Find [tex]\mathbf{B}[/tex] and [tex]\mathbf{H}[/tex] 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,

[tex]\mathbf{H} = \frac{I}{2 \pi\ p}\ \boldsymbol{\hat{\phi}}[/tex]

(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 [tex]\mathbf{B}=\mathbf{H}[/tex]. For a < p < b, we have [tex]\mathbf{B} = \mu\ \mathbf{H}[/tex].

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

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# Magnetostatics problem: find B and H

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