Potentials of a Classical Point-Charge Moving at the Speed of Light

TL;DR

This paper explores the theoretical potentials of a point-charge moving at light speed, presenting new retarded potentials beyond the classical Lienard-Wiechert solutions within special relativity.

Contribution

It introduces novel retarded four-potentials for a point-charge traveling at the speed of light, expanding the understanding of electromagnetic potentials in relativistic contexts.

Findings

New retarded potentials for light-speed charges are derived.

Classical potentials are shown to be a subset of a broader solution set.

The analysis broadens the theoretical framework of electrodynamics at relativistic speeds.

Abstract

Retarded potentials of a point-charge are considered, and new ones presented, including potentials of a point-charge moving at the speed of light. The Lienard-Wiechert potential (together with the usual retardation condition) is only one of many retarded four-potentials that satisfy the homogeneous wave equation and the Lorenz Gauge condition in free space. This analysis is in the context of Special Relativity and classical electrodynamics.