A Spherical Version of Feynman's Static Field Momentum Example

TL;DR

This paper simplifies Feynman's static electromagnetic field momentum example using a spherical geometry, making it more pedagogically accessible and providing insights into the nature of electromagnetic momentum.

Contribution

It introduces a spherical geometry for Feynman's example, allowing closed-form calculations and challenging the inertial mass flow interpretation of electromagnetic momentum.

Findings

Initial and final angular momentum are equal in the spherical model.

The geometry provides a counterexample to the inertial mass flow explanation.

Calculations are accessible with standard upper-division electrodynamics methods.

Abstract

The Feynman demonstration that electromagnetic field momentum is real-even for static fields-can be made more pedagogically useful by simplifying its geometry. Instead of Feynman's disk with charged balls on its surface, this article uses the geometry of a hollow non-conducting sphere with uniform surface charge density. With only methods available in a typical upper-division electrodynamics course, the initial field angular momentum and the final mechanical angular momentum can then be calculated in closed form and shown to be equal. This simplified geometry also provides a counterexample for the idea that electromagnetic field momentum is due to the flow of an electromagnetic inertial mass, defined as the energy density divided by the square of the speed of light. The curved flow lines of an inertial field momentum would require a centripetal force to bend them, but no such force can be identified.