On Magnetic Forces and Work

In this letter, we review a manifestly covariant Lagrangian formulation for the dynamics of a classical particle with intrinsic spin and elementary electric and magnetic dipole moments. We then couple the particle to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle's dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle's permanent magnetic dipole moment. As additional support for this last claim, we calculate the overall system's energy-momentum and angular momentum from Noether's theorem and show that their local conservation equations lead to precisely the same force law. We conclude by computing the system's Belinfante-Rosenfeld energy-momentum tensor.