3D Diagonalization and Supplementation of Maxwell's Magneto-Static Field Equations in Fully Anisotropic and Inhomogeneous Media - Part II: Relative Proof of Consistency

摘要

Consider the Maxwell's magneto-static equations ∇×H=J and ∇·B=0 in fully anisotropic and inhomogeneous media characterized by the 3 × 3 positive-definite position-dependent permeability matrix μ^3×3(x, y, z). In the accompanying paper (Part I) the existence of the diagonalized Dc - and the associated supplementary Sc -forms was demonstrated constructively. In this paper the internal consistency of the (Dc, Sc) - forms is established rigorously by proving the sharp equivalence of the (Dc, Sc) -forms with the originating Maxwell's and constitutive equations.