Uniqueness of Electromagnetic Fields Using Velocity-Dependent Gauge Potentials

This communication is a condensed version of the work by Giri et al. (2022). Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. Common gauges are those named for Lorenz and Coulomb, both of which are special cases of what is termed the velocity gauge, or
$v$
-gauge, where
$v$
is an arbitrary complex propagation velocity. This generalized gauge is not usually taught to students of electrodynamics. In this communication, we briefly describe the
$v$
-gauge, including EM field invariance, and demonstrate its application via an example.