The Electrostatic Energy of a Two-Dimensional System

Abstract

The use of the complex variable z ( = x + iy ) and the complex potential W (= U + iV ) for two-dimensional electrostatic systems is well known and the actual system in the ( x , y ) plane has an image system in the ( U , V ) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the ( U , V ) plane.