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Math Help - Mutual inductance problem

  1. #1
    Member
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    Jan 2010
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    133

    Unhappy Mutual inductance problem

    Hello everyone!

    I'm really stuck on this electromagnetics problem:
    Determine the mutual inductance between an infinite wire and an equilateral triangle-shaped loop as shown in the figure.

    Now, I tried putting current on the long wire so I get \vec{B}=\frac{\mu_0 I}{2\pi r}\vec{a_{\phi}} or in cartesian coordinates \vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}.
    Then I have to dot \vec{B} with \vec{dA} and integrate to find the flux, but that involves a lot of calculation and will carry an \tan^{-1} somewhere, and non of the answers contain a \tan^{-1} but rather a \ln.
    So what to do?
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  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
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    India
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    648
    your expression
    \vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}
    is wrong.
    Since it is infinite in y-direction, the correct expression will be:
    \vec{B}=\frac{\mu_0 I}{2\pi x}\vec{k} where x-axis is from left to right
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