Analytic Magnetic Fields and Semi-Analytic Forces and Torques Due to General Polyhedral Permanent Magnets

This article outlines an algorithm which analytically calculates the magnetic field produced by a general polyhedral permanent magnet with any number of faces and arbitrary face orientations, then uses the algorithm to semi-analytically calculate the force and torque on a second general polyhedral magnet. The algorithm is validated against both the literature and finite element simulations using cuboids and dodecahedra. It is then used to model a basic two-magnet repulsive system, where it is shown that frustum magnets can produce a larger force per unit volume than cuboidal magnets. The shape of the frustums is optimized to maximize the force between them at a given separation distance, showing a considerable increase in force when compared with cuboidal magnets with the same volume. This article shows that there is scope to improve the performance of magnetic systems by using novel magnet shapes and presents an algorithm which can be used for this optimization process.