An exact two-dimensional model for a periodic circular array of head-to-head permanent magnets

An analytical expression is derived for the magnetic field of a two-dimensional periodic circular array of head-to-head permanent magnets, assuming there is either no gap between the magnets or that they are separated by a non-magnetic pole-piece. Some more general symmetry properties are described. The force experienced by the magnets is calculated and an analytical approximation is derived. We comment on the published dipole-approximation used for dealing with this kind of problem and also correct some mistakes.