A formal interpretation of the displacement current and the instantaneous formulation of Maxwell's equations

TL;DR

This paper clarifies the nature of displacement and induction currents, showing their contributions to electromagnetic fields and proposing an instantaneous formulation of Maxwell's equations with local and nonlocal sources.

Contribution

It provides a formal interpretation of displacement and induction currents, distinguishing them from conduction currents and introducing an instantaneous Maxwell's equations formulation.

Findings

Displacement current contributes to magnetic fields.

Induction current contributes to electric fields.

Displacement and induction currents are nonlocal and differ from conduction currents.

Abstract

Maxwell's displacement current has been the subject of controversy for more than a century. Questions on whether the displacement current represents a true current like the conduction current and whether it produces a magnetic field have recently been discussed in the literature. Similar interpretations for the Faraday induction current have also been controversial. These basic questions are answered in this paper by considering the relation between the displacement and conduction currents as well as the relation between Faraday induction and conduction currents. It is pointed out that the displacement current contributes to the magnetic field and that the induction current contributes to the electric field. However, the displacement and induction currents cannot be considered as the conduction current because they are nonlocal. Both relations are used to implement an instantaneous formulation of Maxwell's equations with local and nonlocal sources.