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Magnetostatics problem: find B and H

  1. Sep 5, 2011 #1
    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)?
  2. jcsd
  3. Sep 6, 2011 #2

    rude man

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    Homework Helper
    Gold Member

    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.
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