Torque on an electric/magnetic dipole in the relativistic limit

Abstract

Using a covariant expression for the Lagrangian density of a polarized/magnetized material medium in an electromagnetic field (M. Fabrizio and A. Morri, Electromagnetism of Continuous Media (Oxford University Press, Oxford, 2003)), we derive for the first time in the classical framework the Lorentz-invariant expression for the torque exerted on an electric/magnetic dipole in the presence of electric and magnetic fields and discuss its implications. In particular, we show that in the strong relativistic limit, where the Lorentz factor associated with the moving dipole becomes much larger than unity, the torque terms with an explicit dependence on the velocity of dipole can remain comparable with the well-known terms p x E and m x B, where p, m are the electric and magnetic dipole moments, and E, B are the electric and magnetic fields, correspondingly.