The Coulomb static gauge

TL;DR

This paper introduces the Coulomb static gauge in classical electrodynamics, where the scalar potential is the Coulomb static potential, providing explicit expressions for potentials that produce retarded fields, and relates it to the temporal gauge.

Contribution

It presents a new gauge condition involving second-order derivatives, explicitly derives the vector potential, and clarifies its relation to the temporal gauge.

Findings

Scalar potential equals Coulomb static potential

Explicit vector potential expression derived

Retarded electric and magnetic fields obtained

Abstract

The existence of gauge conditions involving second-order derivatives of potentials is not well known in classical electrodynamics. We introduce one of these gauges, the Coulomb static gauge, in which the scalar potential is given by the Coulomb static potential. We obtain an explicit expression for the associated vector potential and show how the scalar and vector potentials in this gauge yield the retarded electric and magnetic fields. We note the close relation between the proposed gauge and the temporal gauge.