Energy creation in a moving solenoid?

TL;DR

This paper investigates how electromagnetic energy in a moving solenoid transforms relativistically, resolving apparent paradoxes by analyzing the stresses and total energy transformation.

Contribution

It provides a detailed relativistic analysis of energy transformation in a moving solenoid, including stress considerations, to clarify energy accounting.

Findings

Total energy of the moving solenoid transforms by the relativistic factor gamma.

The apparent increase in electromagnetic energy is explained by stresses in the solenoid structure.

The analysis resolves the paradox of energy transformation in moving electromagnetic systems.

Abstract

The electromagnetic energy $U_{em}$ stored in the magnetic field of an ideal solenoid at rest appears for a moving observer as $U'_{em} $, a sum of magnetic and electric energies satisfying: $U'_{em} > \gamma U_{em}$. We explain this seemingly paradoxical result calculating the stresses in the solenoid structure and showing that the total energy of the solenoid transforms by the expected relativistic factor $\gamma$.