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Magnetization of water surrounding submerged non-magnetic wire

  1. Nov 3, 2013 #1
    1. The problem statement, all variables and given/known data
    A long straight wire of circular cross section with radius R carries current I and is immersed
    in a large volume of water. The wire is non-magnetic. Calculate the magnetization M(r) in
    the water which has a susceptibility χm. What is the bound current density Jb(r) for s > R. Calculate the total current (free plus bound).


    2. Relevant equations
    H = [itex]\frac{1}{\mu0}[/itex]B - M
    [itex]\oint[/itex]B [itex]\bullet[/itex] dl = [itex]\mu[/itex]0Ienc
    [itex]\oint[/itex]H [itex]\bullet[/itex] dl = If, enc
    M = [itex]\chi[/itex]mH
    Jb = ∇ × M

    3. The attempt at a solution
    This is how I am thinking about it... the magnetization in the water arises from the current (and resultant B-field) carried by the wire, so I feel like I should calculate the B-field cause by the wire with Ampere's law but then I am unsure of how to use that to find the magnetization in the water.
     
  2. jcsd
  3. Nov 3, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    Hello, GoliathPSU. Welcome to PF!

    Start by finding an expression for H outside the wire as a function of the distance r from the central axis of the wire.
     
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