# Deriving equation for the magnetic field of a variable gap magnet

1. Apr 9, 2009

### CentreShifter

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:

$$B_{ext}=\frac{mg}{lR}\left(\frac{d}{i}\right)$$

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:

$$B=\frac{mg}{iLsin\theta}$$

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 $$l$$ and $$L$$ may be the same variable, but I'm not sure. I've also been told to observe that for small angles $$sin\theta \approx tan\theta$$. Any help would be appreciated.

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