Electromagnetic Forces and Fields in a Rotating Reference Frame

TL;DR

This paper derives Maxwell's equations and charged particle dynamics in a rotating frame, highlighting ambiguities and an extra Lorentz force term, with implications for pulsar magnetosphere models and observed braking indices.

Contribution

It provides a detailed formulation of electromagnetic laws in a rotating reference frame, revealing essential ambiguities and an additional force term affecting pulsar magnetosphere modeling.

Findings

Extra Lorentz force term due to relativistic mass in rotating frames

Ambiguities in defining electromagnetic fields are crucial in rotating coordinates

Potential modifications to pulsar models to better match observed braking indices

Abstract

Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant entities in these equations. Ambiguities in the definitions of the electromagnetic fields are pointed out, and in fact are shown to be essential in such a system of coordinates. The Lorentz force is found to have an extra term in this frame, which has its origins in relativistic mass. A related term in the energy equation, which allows inertia to be gained even during strict corotation, suggests ways existing pulsar magnetosphere models may be modified to match observed `braking indices' more closely.