Maxwell’s displacement current and the magnetic field between capacitor electrodes

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 the Ampere-Maxwell 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.