Finding forces/torques on a permanent magnet from a coil

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I want to know what methods there are for calculating forces by a current-carrying coil on a permanent magnet (the application I have in mind is electrical motors). I.e. given a geometry (like a CAD model of the magnet), the magnet type (e.g neodymium), and wire coil geometry, how are the forces calculated?

I tried looking for some papers but had no luck. I'll appreciate any pointers. Thanks!
 

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