Force on slowly moving variable electric or magnetic dipoles in vacuo

TL;DR

This paper analyzes the forces on slowly moving electric and magnetic dipoles in vacuum under time-variable fields, emphasizing symmetry, interpretation, and proposing an experiment to verify dual-Lorentz forces.

Contribution

It provides a comprehensive analysis of forces on moving dipoles in vacuo, highlighting symmetry and interpretation, and proposes an experiment to test dual-Lorentz forces.

Findings

Symmetry between electric and magnetic dipoles justified

Different forms of force expressions with physical interpretations

Proposal for an experiment to verify dual-Lorentz force

Abstract

The force on electric and magnetic dipoles moving in vacuo is discussed in the general case of time-variable non-uniform fields and time-variable dipole moments, to first order in v/c and neglecting radiation reaction. Emphasis is given to the symmetry between electric and magnetic dipoles, justifying in general Amp\`ere's equivalence principle, and showing that the difference between gilbertian and amperian dipoles (in vacuo) is only a question of interpretation. The expression for the force can be expressed in a variety of different forms, and each term of each form is susceptible of specific physical interpretations. Terms not described in the literature are pointed out. A possible experiment for verifying the (dual-Lorentz) force of an electric field on a magnetic current (and then "hidden momentum") is proposed.