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Mutual Inductance of coaxial coils

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Not sure if I'm correct or wrong..because usually M12 = M21

    3. The attempt at a solution

    Here coil 1 and coil 2 are coaxial, with coil 2 being shorter and having smaller area.

    257lu8x.jpg
     
  2. jcsd
  3. Mar 18, 2013 #2

    rude man

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    M21 always = M12. That can be shown by an energy argument.

    It's correct I think to say that
    M21 = N2phi1/i1. That computes to
    M21 = N2A2μn1
    where N2 is the number of turns in the inside coil 2. This agrees with your expression of M12 (I think you reverse the conventional sequence of the subscripts, but OK).

    This is because the flux inside coil 2 is clearly very nearly the same as that inside coil 1.

    It's more difficult to argue in the same manner to derive M12 because the question is how much of the flux generated by coil 2 really couples into coil 1.

    The answer however has to be such that M12 = M21. I have looked at several derivations of mutual inductance of various coil configurations and in each case they pick the easier computation for Mij and then assume (correctly) that Mji = Mij.
     
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