Revisiting the charging-capacitor problem

TL;DR

This paper reexamines the classical charging capacitor problem, focusing on the conditions for the Faraday-Henry law inside and outside the capacitor, and proposes a recursive method for approximate solutions of Maxwell's equations.

Contribution

It introduces a recursive process to obtain approximate solutions to Maxwell's equations for the charging capacitor, highlighting overlooked aspects of the Faraday-Henry law.

Findings

Identifies overlooked conditions for the Faraday-Henry law in capacitor analysis.

Develops a recursive method for approximate solutions of Maxwell's equations.

Provides insights into the electromagnetic behavior of charging capacitors.

Abstract

The charging capacitor is used as a standard paradigm for illustrating the concept of the Maxwell "displacement current". A certain aspect of the problem, however, is often overlooked. It concerns the conditions for satisfaction of the Faraday-Henry law both in the interior and in the exterior of the capacitor. In this article the situation is analyzed and a recursive process is described for obtaining (at least approximate) solutions of Maxwell's equations inside and outside the capacitor.