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I am studying a motor design that has a cylindrical magnet surrounded by a coil of wire with flowing current. The coil will be fixed/stationary and the magnet will be free to rotate. In the image below, the coil has return legs on either side to form a closed loop. This image represents a cross-section through the center of the magnet and coil.

Calculating the resultant torque on the coil of wire itself is straightforward (T = IAB) but since the coil is stationary, the working torque will actually be transferred to the magnet. I'm not sure how to calculate the torque on the magnet. All of the equations I can find relate to the force on a moving charge in a magnetic field, but I am unable to find any equations for the reaction force on the magnet itself.

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  • $\begingroup$ Newton's third law? $\endgroup$
    – Farcher
    Commented Nov 22, 2022 at 5:59

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I think that you are looking for the magnetic dipole moment. There is a good explanation on the K&J Magnetics blog, link. It can be complicated but it seems easy enough to calculate if you have all the dimensions of the magnet and the properties of the magnet material. There are some good demonstrations of this in the Halbach Arrays 2 blog post as well, link.

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