Hidden Momentum in a moving Capacitor

TL;DR

This paper explores how a moving parallel-plate capacitor exhibits hidden electromagnetic momentum and energy, affecting its overall momentum and energy accounting when viewed from different inertial frames, especially during discharging.

Contribution

It demonstrates the presence of hidden momentum and energy in a moving capacitor and clarifies their role in the system's total momentum and energy accounting, including heat mass effects.

Findings

Hidden momentum and energy appear in moving capacitors.

Energy and momentum transfer between electromagnetic and material parts.

Heat produced during discharge affects mass and energy calculations.

Abstract

A very simple system like a parallel-plate capacitor reveals striking features when we examine the peculiar phenomena appearing when it is moving at low speed in different directions. Both hidden momentum and hidden energy appear and their addition, with their sign, to the corresponding electromagnetic component results in the expected ordinary kinetic momentum or energy of the electrostatic mass equivalent. What's happening is that passing from one inertial reference frame to another, part of the energy or momentum is transferred from the electromagnetic component to the material part of the system or the other way around. A paradoxical self-accelerating behavior is evidenced if one admits that the capacitor is discharging through an electrical resistance during its motion. It is shown that one must take into account the mass of the produced heat.