Interaction of a Point Charge and a Magnet: Comments on "Hidden Mechanical Momentum Due to Hidden Nonelectromagnetic Forces"

TL;DR

This paper investigates the interaction between a point charge and a magnetic moment, clarifying the role of external forces in generating hidden mechanical momentum and questioning its physical significance.

Contribution

It provides explicit calculations showing how external constraint forces create hidden mechanical momentum, challenging its interpretation in existing literature.

Findings

External forces induce hidden mechanical momentum in charge-magnetic systems.

Dependence on external forces questions the physical reality of hidden momentum.

Highlights inaccuracies in textbook explanations of hidden momentum.

Abstract

The interaction of a point charge and a magnetic moment (and by extension a point charge and a solenoid) is explored within well-defined point-charge magnetic-moment models where full calculations are possible. It is shown explicitly how the "hidden mechanical momentum" is introduced by the "hidden" external forces of constraint, requiring a prescribed response (through order 1/c^2) of the system to electromagnetic forces. These external forces often go unmentioned in the textbook and research literature. The dependence of "hidden mechanical momentum" upon detailed external (nonelectromagnetic) forces may undermine the idea's usefulness in describing nature. Some statements of dubious validity in the textbook literature are noted.