Simplified equations for the magnetic field due to an arbitrarily-shaped polyhedral permanent magnet

Abstract Due to their wide use in industrial and commercial devices, it is important to accurately and effectively model permanent magnets, leading to better magnet designs and more desirable magnetic characteristics. In recent decades, researchers have derived equations describing magnetic fields, forces, and torques, but these are usually limited to cuboid or ring-shaped magnets. Some authors have derived magnetic field equations for polyhedral magnets, allowing more general magnet shapes, but these are either not fully simplified or computationally inefficient. This paper presents a new set of simplified and exact equations describing the magnetic field produced by an arbitrarily-shaped polyhedral permanent magnet with constant uniform magnetisation and a relative permeability of unity. These equations were implemented in Matlab code and validated using finite element simulations and literature. These equations are significantly faster than finite element simulations, and can therefore be used for efficient optimisation of magnet geometry or topology, real-time simulations, and for approximation of curved surfaces of permanent magnets.