Three-dimensional derivation of the electrodynamic jump conditions and momentum-energy laws at a moving boundary

The purpose of this paper is to set forth a comprehensive three-dimensional derivation of the electromagnetic jump conditions at a moving boundary. Also presented are corresponding derivations for the electromagnetic surface traction and power transfer formulas. The derivations are based on a variation of an old technique which dates back to Lorentz' introduction of kinematic axioms for electrodynamics. The surface of electromagnetic discontinuity is allowed to move and deform in an arbitrary manner. In addition to the Helmholtz vector-flux theorem which Lorentz employed, two kinematic theorems are utilized in conjunction with Maxwell's equations. Surface charge and surface current are retained in the derivation. These have a marked effect on the current boundary condition and on the surface traction and power transfer formulas. A clear distinction is made between the material velocity and the abstract velocity symbol appearing in the Lorentz integral axioms. New modifications based on this distinction permit derivation of the boundary conditions in a general form applicable to any moving surface of electromagnetic discontinuity, irrespective of the ambient motion of the material medium.