Maxwell equations in material form

Abstract

The Maxwell electromagnetic equations are obtained expressed in the material coordinate system of elasticity theory for a moving, deforming body. They are shown to be form-invariant to the deformation transformation. The transformation laws for the electric field, the electric displacement, the magnetic induction, the magnetic intensity, the charge density, the current density, the vector and scalar potentials, the polarization, and the magentization are found. The boundary conditions on the fields are derived in the material coordinate system and the simplicity of the derivation for moving, deforming bodies is emphasized. The boundary conditions are then transformed to the familiar spatial coordinate system. A Lagrangian density capable of giving the Lorentz form of the electromagnetic equations in the material coordinate system is found. The Lorentz form of the equations is shown not to be form-invariant to the deformation transformation.