Velocity Gauge Potentials in Electrodynamics

TL;DR

This paper reviews the velocity gauge in electrodynamics, discussing its properties, invariance, and applications, highlighting its generality beyond the commonly used Lorenz and Coulomb gauges.

Contribution

It introduces and explains the velocity gauge as a generalized gauge in electrodynamics, which is less commonly taught but offers a broader framework.

Findings

Velocity gauge unifies Lorenz and Coulomb gauges.

Electromagnetic fields are invariant under the velocity gauge.

An example demonstrates the practical application of the velocity gauge.

Abstract

Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. The potentials are made unique by choosing a non-unique gauge relationship. The most commonly used gauges are those named for Lorenz and Coulomb, both of which may be defined as special cases of what is termed the velocity gauge, or v-gauge. This generalized gauge is not usually taught to students of electrodynamics. In this paper, we review properties of the velocity gauge, including EM field invariance, and demonstrate its application via an example.