The Theory of Electrodynamics in a Linear Dielectric

Abstract: We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for D'Alembert's principle and the Lagrange equations. The principles of dynamics in the dielectric-filled space are then applied to the electromagnetic Lagrangian and we derive equations of motion for the macroscopic fields. A direct derivation of the total energy--momentum tensor from the field strength tensor for the electromagnetic field in a dielectric is used to demonstrate the utility of the new theory by resolving the century-old Abraham--Minkowski electromagnetic momentum controversy in a way that preserves the principles of conservation of energy, conservation of linear momentum, and conservation of angular momentum.