The electromagnetic momentum of static charge-current distributions

TL;DR

This paper investigates the origin and nature of electromagnetic momentum in static charge-current distributions, demonstrating how it arises from external forces and clarifying misconceptions about hidden momentum and the center of energy theorem.

Contribution

It provides a derivation of electromagnetic momentum for static fields using momentum conservation and clarifies the roles of external forces and hidden momentum.

Findings

Electromagnetic momentum originates from external forces during static configuration formation.

The center of energy theorem is violated by electromagnetic momentum.

Hidden momentum is generally absent and does not cancel electromagnetic momentum.

Abstract

The origin of electromagnetic momentum for general static charge-current distributions is examined. The electromagnetic momentum for static electromagnetic fields is derived by implementing conservation of momentum for the sum of mechanical momentum and electromagnetic momentum. The external force required to keep matter at rest during the production of the final static configuration produces the electromagnetic momentum. Examples of the electromagnetic momentum in static electric and magnetic fields are given. The `center of energy' theorem is shown to be violated by electromagnetic momentum. `Hidden momentum' is shown to be generally absent, and not to cancel electromagnetic momentum.