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We examine the force of the electromagnetic radiation on linear, isotropic,homogeneous media specified in terms of their permittivity epsilon andpermeability mu. A formula is proposed for the electromagnetic Lorentz force onthe magnetization M, which is treated here as an Amperian current loop. Usingthe proposed formula, we demonstrate conservation of momentum in several casesthat are amenable to rigorous analysis based on the classical Maxwellequations, the Lorentz law of force, and the constitutive relations. Ouranalysis yields precise expressions for the density of the electromagnetic andmechanical momenta inside the media that are specified by their (epsilon, mu)parameters. An interesting consequence of this analysis is the identificationof an "intrinsic" mechanical momentum density, ExM/c^2, analogous to theelectromagnetic (or Abraham) momentum density, ExH/c^2. (Here E and H are themagnitudes of the electric and magnetic fields, respectively, and c is thespeed of light in vacuum.) This intrinsic mechanical momentum, associated withthe magnetization M in the presence of an electric field E, is apparently thesame "hidden" momentum that was predicted by W. Shockley and R.P. James nearlyfour decades ago.

Radiation pressure and the linear momentum of the electromagnetic field in magnetic media