Coupling the Minkowski's theory with the Maxwell's equations for a mechano-driven media system for engineering electromagnetism

Abstract

The Minkowski's theory is regarded as the classical approach for describing the electromagnetism of uniformly moving objects by elegantly utilizing the format-invariance of the Maxwell's equations in inertia reference frames under Lorentz transformation. However, in practice, we usually have the cases of a medium that has boundary and moves with acceleration, such as a rotating dielectric disc or a magnetic object. To fully describe the electromagnetic behavior of such a system, we have developed the Maxwell's equations for a mechano-driven media system (MEs-f-MDMS). This paper is to expand the Minkowski's approach for deriving the constitutive equations and the boundary conditions for MEs-f-MDMS under low-speed approximation (v << c), based on which the equations can be properly solved for describing engineering electromagnetism, with considering the coupling among electric field - magnetic field - mechanical force field. In practice, mechanical action is not merely passive motion through space but an active source of electromagnetic generation and modulation. Our theory makes it possible to treat the electrodynamics by including medium deformation, strain gradients, rotational dynamics, and interfacial contact processes in the full calculation.