Field of a moving locked charge in classical electrodynamics

TL;DR

This paper resolves the paradox of the electromagnetic field of a moving locked charge by analyzing average fields, showing they are independent of motion and consistent with static charge distributions.

Contribution

It demonstrates that average electric fields of locked charges are unaffected by their motion, providing a new understanding of electromagnetic fields in confined systems.

Findings

Average electric field of locked charges is independent of their motion.

Protons in nuclei have the same average electric field as at rest.

Twisted electron's electric field matches that of a static charge distribution.

Abstract

The paradox of a field of a moving locked charge (confined in a closed space) is considered and solved with the use of the integral Maxwell equations. While known formulas obtained for instantaneous fields of charges moving along straight and curved lines are fully correct, measurable quantities are average electric and magnetic fields of locked charges. It is shown that the average electric field of locked charges does not depend on their motion. The average electric field of protons moving in nuclei coincides with that of protons being at rest and having the same spatial distribution of the charge density. The electric field of a twisted electron is equivalent to the field of a centroid with immobile charges which spatial distribution is defined by the wave function of the twisted electron.