Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry

The magnetic field of a permanent magnet is calculated analytically for different geometries. The cases of a sphere, cone, cylinder, ring and rectangular prism are studied. The calculation on the axis of symmetry is presented in every case. For magnets with cylindrical symmetry, we propose an approach based on an expansion in Legendre polynomials to obtain the field at points off the axis. The case of a cylinder magnet was analyzed with this method by calculating the force between two magnets of this shape. Experimental results are presented too, showing a nice agreement with theory.