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Magnetic field question

  1. Feb 23, 2008 #1
    First up, I have got the answer required - however I don't know why this has produced the right answer. I thought it might and tried it, but I don't know why it worked! I would appreciate some insight.

    1. The problem statement, all variables and given/known data
    A small coil of N turns and area A carrying a constant current I and a circular ring with radius R have a common axis. The small coil moves along the axis so that it's distance from the centre of the ring is given by d = d0 + acoswt. Show that the EMF induced in the ring is

    (3/2) mu NAIw aR^2 d (R^2 + d^2)^(-5/2) sinwt


    2. Relevant equations



    3. The attempt at a solution

    OK so for some reason, it worked when I switched the problem around - I said the current is in the ring, not the coil. Then from a previous problem I knew the magnetic field due to current in the ring at any point on its axis is in the direction of the axis and magnitude

    0.5 mu IR^2 (R^2 + x^2)^(3/2)

    As the coil is small, the field can be considered constant across it's cross-section, and along it's length, so each turn has the same uniform field through it and the total flux linkage is

    0.5 Nmu IR^2 (R^2 + d^2)^(3/2)

    Then I differentiated to get the EMF and the answer comes out.

    But why am I allowed to pretend the current is in the ring instead of the coil? Is it something to do with mutual inductance?

    Thanks
     
  2. jcsd
  3. Feb 23, 2008 #2
    Spot on! This is one of those problems where a direct solution would be miserable, but become very simple when invoking the argument of mutual inductance.
     
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