Both necessary and sufficient conditions are derived in a systematic, rigorous way for an electromagnetic constitutive relation to satisfy two fundamental principles: the principle of frame indifference and the second law of thermodynamics. This yields a general theory of constitutive relations which generalizes the classical Ohm's and Hooke's laws in the sense that it can be used for a medium in relative motion. Also developed is a linear theory which reduces three functions in the general theory to three material coefficients.
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