Maxwell’s theory of eddy currents in thin conducting sheets, and applications to electromagnetic shielding and MAGLEV

Using the example of a monopole that is spontaneously generated above a thin conducting sheet, the simplicity and power of Maxwell’s 1872 theory of eddy currents in thin conducting sheets is illustrated. This theory employs a receding image construction, with a characteristic recession velocity v0=2/(μ0σd), where the sheet has conductivity σ and thickness d. A modern derivation of the theory, employing the magnetic scalar potential, is also presented, with explicit use of the uniqueness theorem. Also discussed are limitations on the theory of which Maxwell, living in a time before the discovery of the electron, could not have been aware. Previous derivations either have not appealed explicitly to the uniqueness theorem, or have employed the now unfamiliar current function, and are therefore either incomplete or inaccessible to the modern reader. After the derivation, two important examples considered by Maxwell are presented−a monopole moving above a thin conducting sheet, and a monopole above a rotating ...