Hello, mechanical engineering grad student here. For my project I am working with an iron-cored electromagnet and trying to levitate a permanent magnet beneath it using various control techniques. I have a mathematical model that works pretty well, however I don't think it's as accurate as it could be. In particular I would like to better characterize the forces between the permanent magnet and the iron core of the electromagnet.
Right now I am using the equations for force between two magnetic dipoles, which goes like F~1/x4. This works well for the force between the permanent magnet and electromagnet as long as the permanent magnet is far enough away to approximate both as dipoles. However this only kind of works for the permanent magnet/core force, and my experimental data and FEA data fits a bit better with a curve like F~1/x7. This makes me think there is something more going on, since I would think the core would become more magnetized as the magnet gets closer... I don't really know, but I'd like to have a physical basis for my curve fits.
Can anyone point me to some kind of resource that shows how to get this force relationship? My background on electromagnetic theory is not as strong as I would like so I feel like there is some kind of surface integral formula that would work, I just can't figure out which. If there's another community/subreddit I could post this question in to get a better answer, let me know.
Thanks!
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