Magnetoelectric Ponderomotive Force

The dynamics of a system consisting of a matter continuum with a weak linear magnetoelectric coupling interacting with electromagnetic fields is examined on a local scale in a non-relativistic limit. A consistent expression for the internal energy of the system is derived. The internal energy density and the continuity equation for the momentum lead to the derivation of ponderomotive forces. A non-uniform magnetoelectric coupling generates a "magnetoelectric'' ponderomotive force that could be distinguished from the purely electric or magnetic ponderomotive forces by applying alternating electric and magnetic fields at distinct frequencies.