Energy creation in a moving solenoid?

Abstract

The electromagnetic energy $U_{em}$ stored in the magnetic field of an ideal solenoid at rest appears for a moving observer as $U_{em}^{\prime }$, a sum of magnetic and electric energies satisfying: $U_{em}^{\prime }>\gamma U_{em}$. 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 $\gamma$.

6 pages, 2 figures