Derivation of the Love equation for the charge density of a circular plate condenser

Abstract

The electrostatic problem of two coaxial parallel charged disks of different radii in infinite space is solved by expansion in terms of complex potentials. For perfectly conducting disks a pair of coupled integral equations is derived for the two weight functions of the expansion. The weight function on each disk is linearly related to its radially symmetric charge density. If the radii are equal and the disks are oppositely charged the pair of equations reduce to Love's integral equation for the circular plate condenser.