Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

TL;DR

This paper examines electromagnetic induction forces in different reference frames within relativistic classical electrodynamics, comparing classical and recent formulae for electric fields of moving charges to ensure consistent physical predictions.

Contribution

It demonstrates that recent relativistic formulas provide consistent electromagnetic induction results across reference frames, unlike classical Heaviside formulas.

Findings

Heaviside formula predicts zero inductive force in certain frames

Relativistic formulas yield consistent induction forces in all frames

The study clarifies electromagnetic induction in relativistic contexts

Abstract

The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that, for the particular spatial configuration considered, the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different frames, are given by the recently derived formulae of relativistic classical electrodynamics.