Maxwell's equations for a mechano-driven, shape-deformable, charged-media system, slowly moving at an arbitrary velocity field v(r,t)

TL;DR

This paper derives Maxwell's equations for a slow-moving, deformable, charged media system with arbitrary velocity, extending classical electromagnetism to non-inertial, mechano-driven contexts relevant for fluids and soft media.

Contribution

It provides a new derivation of Maxwell's equations directly from physics laws for media with arbitrary motion and deformation, applicable to a broader class of moving charged media.

Findings

Derived Maxwell's equations for deformable, moving media from first principles.

Presented perturbation-based strategies for solving these equations.

Discussed implications for electrodynamics in non-inertial frames.

Abstract

The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which the medium has a time-dependent volume, shape and boundary and may move at an arbitrary velocity field v(r,t) and along a general trajectory, we derived the Maxwell's equations for a mechano-driven slow-moving media system directly starting from the integral forms of four physics laws, which should be accurate enough for describing the coupling among mechano-electro-magnetic interactions of a general system in practice although it may not be Lorentz covarance. Our key point is directly from the four physics laws by describing all of the fields, the space and the time in the frame where the observation is done. The equations should be applicable to not only moving charged solid and soft media that has acceleration, but also charged fluid/liquid media, e.g., fluid electrodynamics. This is a step toward the electrodynamics in non-inertia frame of references. General strategies for solving the Maxwell's equations for mechano-driven slowing moving medium are presented using the perturbation theory both in time and frequency spaces. Finally, approaches for the electrodynamics of moving media are compared, and related discussions are given about a few interesting questions.