Analytical Calculation of Magnet Systems: Magnetic Field Created by Charged Triangles and Polyhedra

An analytical method for the calculation of the magnetostatic scalar potential and the magnetic field created by a polyhedron-shaped permanent magnet is presented in this paper. The magnet is supposed to be uniformly magnetized. The magnetization is equivalent to distributions of magnetic charges: it is the coulombian approach. The analytical calculation is made by a surface integration on all the polygons that composes the polyhedron. For each polygonal surface, we have shown that it can be decomposed in a series of right triangles. An analytical solution in the particular case of the right triangle has been developed. By this way, the magnetostatic potential and the magnetic field of any polyhedral-shaped magnet can be analytically calculated.