Electromagnetic energy of electric and magnetic dipoles

Abstract

We derive a novel expression for the relativistic energy of electric and magnetic dipoles in an external electromagnetic field and discuss its implications. In particular, we find the relativistic dependence of the energy of a dipole on its velocity, v, and show that in the most convenient presentation of the energy (when the proper electric (p(o)) and magnetic (m(o)) dipole moments are involved, whereas the electric (E) and magnetic (B) fields are defined in the laboratory frame), its value essentially depends on the orientation of the velocity, v, with respect to vectors p(o), E, and m(o), B. To better understand the relativistic behavior of the energy of electric and magnetic dipoles, we introduce the notion of "latent" momentum of an electric dipole, in addition to the known concept of "hidden" momentum of a magnetic dipole. We finally show that the contribution of energy terms related to "hidden" and "latent" momenta of an electric or magnetic dipole is important in the relativistic case.