The Fields of a Charged Particle in Hyperbolic Motion

TL;DR

This paper investigates the peculiar electric field behavior of a charged particle in hyperbolic motion, addressing a longstanding paradox related to Gauss's law and clarifying the reasons behind the failure of naive models.

Contribution

It provides a detailed explanation of why the naive approach to electric fields in hyperbolic motion fails, resolving a sixty-year-old paradox.

Findings

Naive models produce apparent field termination in mid-air.

The resolution involves subtle effects overlooked in simple models.

Clarifies the conditions under which Gauss's law holds for accelerated charges.

Abstract

A particle in hyperbolic motion produces electric fields that appear to terminate in mid-air, violating Gauss's law. The resolution to this paradox has been known for sixty years, but exactly why the naive approach fails is not so clear.