Recent Progress on the Maxwell's Equations for Describing a Mechano-Driven Medium System with Multiple Moving Objects/Media

Maxwell's equations for a mechano-driven media system (MEs-f-MDMS) have been used to characterize the electromagnetism of multi-slow-moving media that may be accelerated with complex trajectories. Such an approach starts from the integral forms of the four physics laws and is different from the classical approach of using the Lorentz transformation for correlating the electromagnetic phenomena observed in two inertial reference frames with relative motion. The governing equations inside the moving object/medium are the MEs-f-MDMS, and those in vacuum are the classical Maxwell's equations; the full solutions of both reconcile at the medium surface/interface and satisfy the boundary conditions. This paper reviews the background, physical principle, and mathematical derivations for formulating the MEs-f-MDMS. Strategies are also presented for mathematically solving the MEs-f-MDMS. The unique advances made by the MEs-f-MDMS have been systematically summarized, as are their potential applications in engineering. We found that the Lorentz transformation is perfect for treating the electromagnetic phenomena of moving point charges in vacuum; however, for moving objects, the covariance of Maxwell's equations may not hold, and use of the MEs-f-MDMS may be required if the velocity is low. Finally, recent advances for treating the boundary conditions at the nanoscale without assuming an abrupt boundary are also reviewed.