A New Energy Conservation Law for Time-Harmonic Electromagnetic Fields and Its Applications

TL;DR

This paper introduces a new energy conservation law for time-harmonic electromagnetic fields applicable to any medium, providing insights into energy storage and transfer, especially in complex media, and extends understanding beyond the classical Poynting theorem.

Contribution

It presents a novel energy conservation law that generalizes the Poynting theorem for arbitrary media, including complex and lossy materials, with explicit expressions for stored energies.

Findings

Derived a universal energy conservation law for time-harmonic fields.

Provided expressions for electric and magnetic field energies in complex media.

Showed the law's implication for energy accounting in lossless isotropic media.

Abstract

We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies and the imaginary part involves an equation related to the difference between the dissipated electric and magnetic energies. Universally applicable expressions for both the electric and magnetic field energies have been obtained and demonstrated to be valuable in characterizing the energy storage and transport properties in complex media. For a lossless isotropic and homogeneous medium, the new energy conservation law implies that the stored electromagnetic field energy of a radiating system enclosed by a surface is equal to the total field energy inside the surface subtracted by the energy flowing out of the surface.