The Coulomb Potential of a Line of Charges

Abstract

Recently Lekner gave formulae for the total Coulomb force and potential on a charged particle due to a line of other charged particles, and showed how to use it for a regular array of charges in two or three dimensions. His method involves a series in terms of the Bessel function Ko which converges fast for points sufficiently far from the line. This paper gives an integral which can be evaluated faster for points close to the line.