Resolution of the Mansuripur Paradox

Abstract

The interaction of a magnetic dipole with a point charge leads to an apparent paradox when analyzed using the 3-vector formulation of the Lorentz force. Specifically, the dipole is subject to a torque in some frames and not in others. We show that when analyzed according to the covariant 4-vector formulation the paradox disappears. The torque that arises in certain frames is connected to the time-space components of the torque in the rest frame, giving rise to "hidden" momentum.