How do I calculate the pull force of a cylindrical electromagnet to Iron as a function of distance?
Is there any difference betweeen magnets and electromagnets?
Answer
It's a very hard problem. If magnetism behaved like gravity, you could break up the plane and magnet into small dipoles and sum up all of the dipole-dipole interaction energies for all possible pairs (this would make a hex-tuple integral!). The force is simply the rate of change of the total energy. However, you need to first calculate the induced magnetization of iron, which is complicated and has a "saturation" behavior. The paper:
http://www.gris.uni-tuebingen.de/people/staff/spabst/magnets/Magnets_in_Motion.html
Lays out the needed calculations. Of course, the cylindrical symmetry will reduce the calculations needed.
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