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Deriving equation for the magnetic field of a variable gap magnet

  1. Apr 9, 2009 #1
    I'm being asked to derive the equation for the magnetic field produced by a variable gap magnet. I've been given a few clues, but thus far have been unable to actually complete the derivation. The final equation should be:

    [tex]B_{ext}=\frac{mg}{lR}\left(\frac{d}{i}\right)[/tex]

    I'm told I need to use the Biot-Savart law and Newton's first (specifically sum of torque = 0).

    I have also gone as far as recognizing that:

    [tex]B=\frac{mg}{iLsin\theta}[/tex]

    is going to be incorporated. This is from the cross product equation for the magnetic force (the force is balancing a current carrying wire within the gap of the magnet). I suspect that [tex]l[/tex] and [tex]L[/tex] may be the same variable, but I'm not sure. I've also been told to observe that for small angles [tex]sin\theta \approx tan\theta[/tex]. Any help would be appreciated.
     
  2. jcsd
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