Electrostatics in the presence of spherical dielectric discontinuities

A united description of the electrostatics of an arbitrary number of electrostatic multipoles, each localized in a spherical dielectric cavity, in a dielectric medium is presented. The permanent charges as well as the polarization surface charges are described by multipole expansions in standard format. Expressions of the polarization surface charge density, the electrostatic potential energy, and the electrostatic interaction including the contribution from the polarization surface charge densities are given. Interacting electrostatic multipoles in dielectric spheres immersed in a medium with a higher (lower) relative dielectric permittivity experience a repulsive (attractive) potential term that increases in magnitude at reduced multipole separation, originating from the polarization surface charges appearing at the dielectric interfaces. Simplified expressions applied to monopoles and to two dielectric cavities are provided. Numerical examples involving monopoles and dipoles quantifying the effect of the surface polarization are also included.