Power-energy & dispersion relations for diamagnetic media

Although diamagnetism in bismuth and antimony was discovered by S.J. Brugmans in 1778 and Michael Faraday coined the word ldquodiamagnetismrdquo in 1845 when he realized that all materials possessed some form of diamagnetic response to an applied magnetic field, classical power-energy relations in a diamagnetic continuum have not been determined. One reason for this is the Bohr-Leeuwen theorem, which is often used to argue that classical electromagnetics cannot describe diamagnetism. This theorem assumes that all the energy at thermal equilibrium is in the kinetic and potential energy of the charge carriers. However, by using a conducting ring/loop model for molecules or metamaterial inclusions, an additional inductive magnetic-field energy is introduced such that the Bohr-Leeuwen theorem no longer applies and we are able to classically derive macroscopic power energy relations in diamagnetic materials and metamaterials.