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Homework Help: Mutual Inductance

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data
    Derive an expression for the mutual inductance ,L12, for the case of the figure, assuming a current distribution:
    J[itex]_{2}[/itex](x)= F[itex]_{2}[/itex](x), h1<x<h2
    I[itex]_{2}[/itex](x)= ∫[itex]^{h_2}_{h_1}[/itex] F[itex]_{2}[/itex](x)w[itex]_{2}[/itex]dx

    2. Relevant equations

    L[itex]_{12}[/itex](x)=∅[itex]_{12}[/itex](x)/ i[itex]_{2}[/itex](x)

    3. The attempt at a solution
    In fact I don't know why the problem gives this current distribution. For me the final expression of the mutual inductance does not depend on current. And I don't know either the behavior of the flux lines. The final expression for the mutual I found is L[itex]_{12}[/itex]=μ[itex]_{0}[/itex]*(h[itex]_{2}[/itex]-h[itex]_{1}[/itex])w[itex]_{1}[/itex] / (g+h[itex]_{2}[/itex])

    Attached Files:

  2. jcsd
  3. Apr 28, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    No idea what this picture represents. Coils? You're right, the mutual inductance between two wired arrangements is not a function of current unless paramagnetics are involved.
  4. Apr 28, 2013 #3
    The problem is not clear at all on specifying what really this picture means. But I guess the region that is in bege is the magnetic core whose permeability is infinity. And 1 and 2 are cross section of rectangular conductors embedded in the core. Then, for somehow, it makes a currrent density to go through a conductor 2 and it will generate a magnetic flux across conductor 1, for this magnetic flux that is mutual inductance associated. That is what a problem is asking for.
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