Field Reactions to Moving Charges

Abstract

The concept of self-force on a moving charge is introduced along with the idea of electromagnetic mass. Lorentz’s calculation of the self-force is presented that yields an analytical form of the self-force on an accelerating sphere of charge. The equations of motion for a charge including self-force are derived, known as the Abraham–Lorentz formula. This formula is applied to sinusoidal motion and constant acceleration and its general solution is shown to result in runaway and pre-acceleration. The Landau–Lifshitz approximation alleviates these issues and the self-force is shown to act only over an experimentally extremely short characteristic time. Additionally, issues include the problem that the dynamically calculated electromagnetic mass is 4/3 the statically calculated one; the introduction of Poincare stresses reconciles this difference. Finally, the infinite electromagnetic mass problem of a point-like particle is shown to be manageable by considering advanced as well as retarded waves in the potentials.