Radiation from charges in the continuum limit

TL;DR

This paper investigates how radiation from accelerating charges diminishes as a system approaches the continuum DC limit, reconciling the apparent contradiction between individual charge radiation and zero radiation in steady currents.

Contribution

It provides a detailed analysis and quantification of the radiation behavior of charges transitioning to the continuum DC limit, clarifying the conditions under which radiation vanishes.

Findings

Radiation from charges decreases as the system approaches the continuum limit.

Steady DC currents in closed loops do not radiate despite individual charges accelerating.

Quantitative measures of radiation suppression in the continuum limit.

Abstract

It is known that an accelerating charge radiates according to Larmor formula. On the other hand, any DC current following a curvilinear path, e.g. a circular loop, consists of accelerating charges, but in such case the radiated power is 0. The scope of this paper is to analyze and quantify how the radiation vanishes when one goes to the continuum DC limit.