Force on slowly moving variable electric or magnetic dipoles in vacuo

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.