Relativistic energy of a moving spherical capacitor

TL;DR

This paper examines how the electromagnetic energy of a moving spherical capacitor transforms under relativity, revealing that it differs from the simple Lorentz factor and ensuring the total energy transformation aligns with relativistic principles.

Contribution

It provides a detailed analysis of the relativistic transformation of energy in a spherical capacitor, including effects of stresses and electromagnetic fields, which was not previously fully understood.

Findings

Total energy transforms according to relativistic principles

Energy in a moving frame differs from gamma times rest energy

Stresses in capacitor shells influence energy transformation

Abstract

We discuss the relativistic transformation of the energy of a charged spherical capacitor. The energy stored in the electromagnetic fields observed by an uniformly moving frame is related to that of the rest frame by a factor different from $\gamma $. Considering the energy and the stresses in the capacitor shells we show that the total energy of the system satisfies the expected relativistic transformation.