On the electrodynamics in time-dependent linear media

TL;DR

This paper investigates classical electrodynamics in homogeneous, time-dependent linear media, revealing new effects such as an additional term in Ampere-Maxwell's law and asymmetries in wave equations caused by permittivity's time variation.

Contribution

It introduces the impact of time-dependent permittivity on electrodynamics, highlighting new terms and asymmetries in fundamental equations.

Findings

Time-dependent permittivity adds an extra term in Ampere-Maxwell law.

Asymmetry between electric and magnetic wave equations arises.

Special cases include linear, exponential, and sinusoidal permittivity variations.

Abstract

In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to an additional term in the Ampere-Maxwell equation and an asymmetry between the electric and magnetic field wave equations. As special cases we consider a linear and an exponential growth of the permittivity, as well as a sinusoidal time-dependent permittivity.