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

Jin Jer Huang

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arXiv · 2511.14492

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

Jin Jer Huang

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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.

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Jin Jer Huang. 2025-11-18. A reinterpretation of classical magnetism via the regular representation of displacement current. https://arxiv.org/abs/2511.14492

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