A derivation of Warburg’s law for point to plane coronas

Abstract

Warburg’s law, which describes the distribution of the current density over the plane electrode for a point to plane steady corona discharge, is derived. The derivation is based on a model using hyperboloid point to plane geometry with a constant charge carrier mobility model and a time independent potential. The derived relation is shown to be in exact agreement with the empirical law when the calculations are done for an infinite plane electrode.