Electromagnetic Field Energy Balance for Dispersive Medium

Abstract

In this paper electromagnetic field energy balance equation for linear homogeneous dispersive stationary medium is deduced in general form. No dispersive limitations on e′, e″, μ′, and μ″ are used. Thus the following question is answered: why do existing equations not provide correct values for accumulated energy and dissipated energy in dispersive media? An electromagnetic field energy balance equation for harmonic processes is obtained. This equation separates into active energy and reactive energy equations. Each of these equations contains four terms. For active energy equation the first two terms determine dissipation energy per unit volume. Each of these two terms can be expressed as a sum of three terms: the first one determines dissipation energy for unit volume without dispersion; the other two terms describe dissipation energy density due to dispersion. The third term is a Poynting vector real part change rate for frequency and coordinate, the last term—determines external source active energy density. The first two terms for reactive energy determine electromagnetic field accumulated energy density per unit volume. Each of these two terms of electromagnetic field accumulated energy density can be expressed as a sum of three terms: the first one determines accumulated energy for unit volume without dispersion; the other two terms are accumulated energy additions due to dispersion. The third term is a Poynting vector imaginary part change rate for frequency and coordinate. The last term—determines external source reactive energy density. Presented electromagnetic field energy characteristics definitions satisfy the second law of thermodynamics.