Applying relativistic electrodynamics to a rotating material medium

We apply relativistic electrodynamics to a rotating linear medium. Covariant field equations are used to derive general field equations in a rotating coordinate system. We argue that the relation between fields in the presence of matter and those in a vacuum is necessarily dependent upon the coordinate system used. Constitutive equations are then derived in the rotating and laboratory reference frames. We find that our constitutive equations in the laboratory frame agree with Minkowski’s constitutive equations, derived on the basis of special relativity in 1908. Thus we conclude that special relativity can be used in the analysis of experiments involving rotational motion. To exemplify the use of special relativity, we derive an experimentally observed result of a 1913 experiment performed by Wilson and Wilson in which a polarizable, permeable cylinder was rotated in a uniform, axially directed magnetic field.