Modeling Earth as a magnet
For reasons best described as 'mad armchair science,' I find myself wondering how to model the repelling force in Newtons between a magnet of
arbitrary field strength BM and the Earth itself. I've tried using this page on Wikipedia, but I'm pretty lost in the math and was wondering if someone could help explain it to me. I know it's going to be very,
very small for any realistic BM value, but I'd like to know how small exactly.
If it makes calculations simpler, one could envision the situation as a magnet positioned at the magnetic south pole of the Earth, with the magnet's
south pole facing directly downward. I've found from other sources that the average magnetic field at the Earth's surface BE varies between 25 and 65 x 10-6 Tesla, and
the rate of change dB/dz is approximately 2.161 x 10-9 Tesla/meter.
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