Surface spreading of charge due to ohmic conduction

Abstract

Exact analytical solutions are presented for the time-dependent charge and potential distributions due to the surface spreading of any initial charge distribution by ohmic conduction on the plane interface between two isotropic insulators of zero bulk conductivity. The solutions are applicable to systems of insulators that extend to infinity, which may include electrodes provided these have infinite surfaces that are normal to the boundary plane between the insulators. The solutions reduce charge spreading problems to ones of simple electrostatics where the time-dependent potential can be treated as being due to the initial charge distribution receding from the interface plane with a constant characteristic velocity. Solutions for the behaviour of various initial charge distributions are given.