The internal field in dipole lattices

Abstract

The internal field for Bravais lattices of equal parallel dipoles having monoclinic and higher symmetry is evaluated. The electric field at a lattice point due to all the other dipoles in the lattice is given by a conditionally convergent sum. It is shown that, when considering a slab of dielectric material in a parallel plate condensor, this ‘dipole sum’ should be summed ‘plane-wise’ in order to obtain the correct contribution to the internal field. Rapidly converging expressions for this contribution are derived. For a simple cubic lattice the resulting expression for the internal field reduces, of course, to that of Lorentz.