On Force Interactions for Electrodynamics-Like Theories

TL;DR

This paper develops a geometric framework for premetric electrodynamics, deriving Maxwell's equations and force interactions independently of constitutive relations, with applications to electrostatics and magnetostatics.

Contribution

It introduces a novel geometric continuum mechanics approach to electrodynamics, providing new expressions for force and stress interactions that differ from standard formulations.

Findings

Derived Maxwell equations from stress theory without constitutive assumptions

Presented new expressions for potential energy, force, and stress in spacetime

Applied framework to electrostatics and magnetostatics examples

Abstract

A framework for premetric p-form electrodynamics is proposed. Independently of particular constitutive relations, the corresponding Maxwell equations are derived as a special case of stress theory in geometric continuum mechanics. Expressions for the potential energy of a charged region in spacetime, as well as expressions for the force and stress interactions on the region, are presented. The expression for the force distribution is obtained by computing the rate of change of the proposed potential energy under a virtual motion of the region. These expressions differ from those appearing in the standard references. The cases of electrostatics and magnetostatics in R^3 are presented as examples.