Potentials of a uniformly moving point charge in the Coulomb gauge**This paper is written by V Hnizdo in his private capacity. No official support or endorsement by the Centers for Disease Control and Prevention is intended or should be inferred.

Abstract

The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand side of the Poisson equation involves an important but easily overlooked delta-function term that arises from a second-order partial derivative of the Coulomb potential of a point charge.