Magnetic Force Formulae for Magnets at Small Distances

In [7], the magnetic force on subregions of rigid magnetized bodies was studied as a discrete-to-continuum limit. The de-rived force formula includes a new term, which depends on the underlying crystalline lattice structure L. It originates from contributions of magnetic dipole-dipole interactions of dipole moments close to the boundary of the considered subregion. Further studies of this new term have led to the question of how the magnetic force between two idealized magnets, which are a distance ε> 0 apart, depends on ε as ε → 0. In this article, analytical aspects of this question are discussed, cf. [5], where also numerical experiments are performed.