A reinterpretation of classical magnetism via the regular representation of displacement current

Abstract

The displacement current, introduced by Maxwell, has long caused confusion regarding its relationship to the magnetic field. To develop a new understanding of classical magnetism, this work first decomposes the displacement current into a localized internal component and an external field distribution by employing a discal regularization of the dipole distribution. Due to a surprising cancellation of the electric current by this internal displacement current, an integral expression for the magnetic field in terms of the external displacement current (or total current) enables a reinterpretation of classical magnetism. Consequently, the current equivalence is resolved and refined through this integral representation in both quasi-steady and quasi-static states. In the latter case, the nonzero external displacement current is exactly equal to---and can easily be mistaken for---the current in the circuit system. This paper proposes a potential solution to several longstanding historical disputes concerning the displacement current.

18 pages, 6 figures, 5 appendices