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H-Field in a region with magnetic susceptibility from an infinite line charge

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Pollack, Stump - Electromagnetism. Prob. 9.23

    A long straight wire carrying current 1 is parallel to the z axis and passes through
    the point (a, 0, 0) . The region x > 0 is vacuum, and the region x < 0 is a material
    with magnetic susceptibility Xm .
    Show that the H-field in the region x < 0 is the same as H that would be produced
    by a current 211(2 + Xm) in the wire with the material everywhere; and the H-field
    in the region x > 0 is the same as H that would be produced by the combination of
    the current 1 in the wire and a current Xm 1 I (2 + Xm) along the line parallel to the z
    axis through (-a, 0, 0), with vacuum everywhere. (Hint: Appeal to the uniqueness
    theorem. What are the boundary conditions?)



    2. Relevant equations

    H = B/μ0 - M

    M = χH

    ∫H dl = I (free, enclosed)


    3. The attempt at a solution

    Ok, so my first thought was to find the H-field in both regions using ampere's law, but won't I have to find the magnetization to be able to find it in the region with the magnetic susceptibility? What is tripping me up is figuring out to solve it with 2 separate regions. Any initial help to get me started would be great. Thanks
     
  2. jcsd
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