Maxwell's Displacement Current and the Magnetic Field between Capacitor Electrodes

TL;DR

This paper clarifies the origins of the magnetic field around a capacitor by analyzing Maxwell's displacement current, addressing misconceptions and emphasizing the distinct roles of electric field components.

Contribution

It provides a detailed examination of the causes of magnetic fields in capacitors, clarifying misconceptions about displacement current and electric field components in Maxwell's equations.

Findings

Displacement current contributes to the magnetic field in capacitors.

Misinterpretations of Maxwell's laws can lead to misconceptions.

Electric field components have distinct roles in electromagnetic phenomena.

Abstract

A long-standing controversy concerning the causes of the magnetic field in and around a parallel-plate capacitor is examined. Three possible sources of contention are noted and detailed. The first is the ambiguous initial impression given by the calculation of the magnetic field using the integral form of Ampere-Maxwell's Law which incorporates the displacement current density. The second is misinterpretation of this law as a cause-effect formula. The third is insufficient recognition of the fact that the electric field in Maxwell's equations represents the sum of the well-distinguished irrotational and divergence-free fields, which are independently responsible for conservation of charge and the existence of the electromagnetic waves, respectively.