Maxwell’s equations for a mechano-driven varying-speed motion media system under slow motion and nonrelativistic approximations

<p indent="0mm">The governing rules of the electromagnetic fields for a moving media system are important for engineering applications and physics. A systematic comparison of special relativity and Galilean electromagnetism is first given. Then, starting from the integral form of the four physics laws, the Maxwell’s equations for a mechano-driven slow-moving media system are derived. Through the coupled mechanical force-electric-magnetic fields, the expanded Maxwell’s equations should reveal the dynamics of an electromagnetic field for a general case, in which the medium has a time-dependent volume, shape, and boundary and may move in an arbitrary, slow-moving velocity field <bold>v</bold>(<italic>r</italic>, <italic>t</italic>) in a noninertial system. A mechano-induced polarization term <bold>P</bold>_S is introduced in the displacement vector to represent the polarization produced by the relative movement of the charged media under an external force. Notably, the additional term <bold>P</bold>_S is different from the medium polarization <bold>P</bold> because of the external electric field <bold>E</bold>; thus, these terms cannot be merged even in mathematical form. Most importantly, the expanded equations may not satisfy Lorentz covariance because the energy of electricity and magnetism is not conservative under external mechanical energy, but the total energy of the closed system is conservative. At last, the charged moving media are confirmed to be sources of generating electromagnetic radiation (a motion-generated electromagnetic field). The generated electromagnetic wave within the medium can be described using the expanded Maxwell’s equations. Its propagation in space can be thoroughly characterized using the standard Maxwell’s equations and special relativity, which meet at the medium interface governed by the boundary conditions.