On the nonradiating motion of point charges

TL;DR

This paper explores conditions under which point charges can move without radiating electromagnetic energy, proving that two charges cannot do so indefinitely, but providing examples of nonradiating accelerated motions.

Contribution

It establishes that two point charges cannot sustain nonradiating motion indefinitely, but demonstrates that nonradiating accelerated motions of multiple charges are possible.

Findings

Two charges cannot move indefinitely without radiating

Nonradiating accelerated motions of charge systems can exist

Examples of nonradiating motions are provided

Abstract

We investigate the possible existence of nonradiating motions of systems of point charges, according to classical electrodynamics with retarded potentials. We prove that two point particles of arbitrary electric charges cannot move for an infinitely long time within a finite region of space without radiating electromagnetic energy. We show however with an example that nonradiating accelerated motions of systems of point charges do in general exist.