# Self-field, radiated energy, and radiated linear momentum of an accelerated point charge (Part 2)

## TL;DR

This paper provides an exact solution for the self-force, radiated energy, and momentum of an accelerated point charge in free space, advancing classical electrodynamics by avoiding mass renormalization.

## Contribution

It derives exact formulas for self-force, radiated energy, and momentum without infinities, and presents two derivations of the Abraham-Lorentz-Dirac equation.

## Key findings

- Exact formulas for radiated energy and momentum
- Derivation of the Abraham-Lorentz-Dirac self-force
- Discussion of Landau-Lifshitz approximation

## Abstract

Working within the framework of the classical theory of electrodynamics, we derive an exact mathematical solution to the problem of self-force (or radiation reaction) of an accelerated point-charge traveling in free space. In addition to deriving relativistic expressions for self electromagnetic fields, we obtain exact formulas for the rates of radiated energy and linear momentum without the need to renormalize the particle's mass - or to discard undesirable infinities. The relativistic expression of self-force known as the Abraham-Lorentz-Dirac equation is derived in two different ways. Certain properties of the self-force are examined, and an approximate formula for the self-force, first proposed by Landau and Lifshitz, is discussed in some detail.

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Source: https://tomesphere.com/paper/1902.02873