Doppler signature in electrodynamic retarded potentials

Abstract

The presence of the term $\left(v/c\right)$ that characterizes the electrodynamic retarded potentials, also known as Liénard–Wiechert potentials, is thought to be reminiscent of a Doppler effect. Here, we show that these potentials are consistent with the Doppler shifted electromagnetic (e.m.) field generated by a charge moving along a generic trajectory. Of course, the retarded potentials derived here are formally the same as those reported in the current literature. Nonetheless, this work sheds a new light on the origin of the electrodynamics retarded fields, offering a direct physical interpretation of the term $\left(v/c\right)$ characterizing the related potentials and making more evident the geometry underlying the radiation field associated to a moving charge. This could inspire new visions for calculating radiation and fields from accelerated charges, including particle physics, Cherenkov radiation and electromagnetic fields in curved space–time.