Image charges revisited: a closed form solution

Abstract

We demonstrate that the corrections to the classical Kelvin image theory due to finite electron screening length $λ$, recently discussed by Roulet and Saint Jean, Am. J. Phys. 68(4) 319, is amenable to an exact closed form solution in terms of an integral involving Bessel functions. An improper choice of boundary conditions is rectified as well, enabling also a complete solution for all potentials - both inside and outside the metal surface.