A Steady Loop Current Does Not Radiate

TL;DR

This paper demonstrates that a steady loop current does not radiate by analyzing the retarded electric and magnetic fields, confirming classical electrodynamics principles through exact integral comparisons.

Contribution

The authors extend previous approximations to exact retarded fields, showing that steady loop currents do not emit radiation and recover classical laws like Coulomb's and Biot-Savart.

Findings

Steady loop currents do not radiate electromagnetic energy.

Exact retarded field integrals match static field expressions.

Classical laws are recovered without approximation.

Abstract

According to classical electrodynamics, a steady loop current does not radiate. Edward, Kenyon, and Lemon show that the present-time approximation of the retarded electric field (the approximation of the magnetic one is trivial) of a steady loop current can be partitioned into a loop integral of a static field expression and a loop integral of an exact (also called total, full, or perfect) differential. Because the latter is zero, no radiation is emitted. Inspired by their work, we do the same for the retarded electric and magnetic fields without approximation, and show that for a steady loop current, the loop integrals of the static field expressions with and without approximation are exactly equal, recovering Coulomb's law and the Biot-Savart law for a steady loop current.