A Steady Loop Current Does Not Radiate
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.
Cite
@article{arxiv.2308.13221,
title = {A Steady Loop Current Does Not Radiate},
author = {Shengchao Alfred Li and Charlotte Jingyang Li},
journal= {arXiv preprint arXiv:2308.13221},
year = {2025}
}
Comments
7 pages, 3 figures. An early version was submitted to American Journal of Physics and said to be correct but aiming at an old problem thus rejected. Added Table 1, computer code (Appendix), Fig. 1; Removed old Sect. 3; Re-written old Sect. 4 (Now II), old Sect. 5 (Now III); Old potential method was replaced with a new easy method starting from textbook equations (Eqs. 13,14)