The force density in polarizable and magnetizable fluids

The force density in polarizable and magnetizable fluids in nonuniform motion is evaluated in a way that is consistent with the special theory of relativity. The derivation is based on a generalization of the principle of virtual work. For application of the principle, it is necessary to know the energy density and power-flow density in a local rest frame of the fluid element under consideration. These are obtained from thermodynamic information and an extrapolation of the Poynting theorem applied to a rigid, nondeforming medium. Two different formulations of electrodynamics of moving and deforming media are compared. It is shown that they lead to the same force density if the same thermodynamic information is used in each of them. A simple model for the force density is obtained, starting from the E-H formulation.