Tracking the radiation reaction energy when charged bodies accelerate

TL;DR

This paper investigates energy conservation during radiation from an accelerating charged particle, clarifying the roles of radiation reaction, the Schott force, and providing a visual method to track radiated energy.

Contribution

It offers a modern analysis of radiation reaction and self-force, resolving paradoxes and clarifying energy accounting in classical electromagnetism.

Findings

Clarifies the influence of the Schott force on energy accounting.

Provides a visual method to track radiated energy without far-field analysis.

Resolves the radiation paradox for uniformly accelerating charges.

Abstract

We address some questions related to radiation and energy conservation in classical electromagnetism. We first treat the well-known problem of energy accounting during radiation from a uniformly accelerating particle. We present the problem in the form of a paradox, and then answer it using a modern treatment of radiation reaction and self-force, as it appears in the expression due to Eliezer and Ford and O'Connell. We clarify the influence of the Schott force and the total radiated power, which differs from Larmor's formula. Finally, we present a simple and highly visual argument which enables one to track the radiated energy without the need to appeal to the far field in the distant future (the 'wave zone').