Electromagnetic Energy of a Small Electric/Magnetic Dipole: Relativistic Limit

Abstract

We derive a relativistic expression for the electromagnetic (EM) energy of a small electric/magnetic dipole in an EM field, using a manifestly covariant expression for the Lagrangian density of a polarized/magnetized material medium in an EM field.13 We discuss possible implications of the obtained result and, in particular, show the perfect fulfillment of the relativistic transformation for the EM four-momentum of the dipole, given that its spatial components are defined as the sum of its "hidden momentum", first introduced by Shockley and James5 and its "latent momentum", first introduced by Kholmetskii et al.10