Self-forces on extended bodies in electrodynamics

TL;DR

This paper investigates how the internal structure of extended charged bodies influences their motion in flat spacetime, revealing significant self-interaction effects beyond classical models, especially under certain charge-current configurations.

Contribution

It develops a formalism to analyze the motion of extended charges with arbitrary shape and internal properties, extending beyond standard assumptions and deriving general equations of motion.

Findings

Large self-interaction effects can occur even with small angular momentum.

Conditions for significant effects include specific charge and current density ratios.

Simplified equations are obtained when considering only radiative self-fields.

Abstract

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.