The unification of the Lorentz and Coulomb gauges of electromagnetic theory

The Lorentz and Coulomb gauges of electromagnetic field theory are shown to be special cases of the same gauge, denoted in this paper as the velocity gauge since it specifies the divergence of the vector potential in terms of the velocity of propagation of the scalar potential. This velocity is the speed of light for the Lorentz gauge and infinite for the Coulomb gauge. With the velocity gauge, the selection of a gauge can be explained in physical terms—the specification of the velocity of propagation of the scalar potential—which engineering students might find more intuitive than a suspiciously arbitrary choice made for mathematical convenience.