Energy and Angular Momentum Storage in a Rotating Magnet

TL;DR

This paper analyzes a rotating cylindrical magnet system, demonstrating how electromagnetic angular momentum, charge accumulation, and energy considerations are essential for understanding its dynamics and energy storage.

Contribution

It provides a detailed Newtonian analysis of electromagnetic angular momentum and energy accounting in a rotating magnet system, highlighting pedagogical value.

Findings

Electromagnetic angular momentum must be included for accurate angular momentum accounting.

Charge accumulation affects radial current and system dynamics.

Potential energy loss relates to electrostatic energy and Joule heating.

Abstract

We consider a cylindrical metallic magnet that is set into rotation about a horizontal axis by a falling mass. In such a system the magnetic field will cause a radial current which is non-solenoidal. This leads to charge accumulation and a partial attenuation of radial current. The magnetic field acting on the radially flowing current slows down the acceleration. Using newtonian dynamics we evaluate the angular velocity and displacement. We explicitly show that the electromagnetic angular momentum must be taken into consideration in order to account for the change in angular momentum due to the external torque on the system. Further the loss in potential energy of the falling mass can be accounted for only after taking into consideration the electrostatic energy and the Joule loss. We suggest that this example will be of pedagogical value to intermediate physics students. A version of this is scheduled to appear in American Journal of Physics 2011. Keywords: Rotating magnet, Charge accumulation