Forces Between a Permanent Magnet and a Soft Magnetic Plate

Forces between a hard/permanent magnet of arbitrary shape and an ideally soft magnetic plate in close proximity are derived analytically from the image method applied to magnetostatics. We found that the contact force, defined as the force required to detach the hard magnet from the plate, coincides with that between two identical touching permanent magnets.

Furthermore, if the hard and the soft magnets are displaced by some amount, their attraction equals that between two identical permanent magnets displaced by twice that amount. Experimental results are presented that validate the theoretical framework and highlight its limits of applicability.