ISSN 1063-7850, Technical Physics Letters, 2006, Vol. 32, No. 11, pp. 982–986. © Pleiades Publishing, Inc., 2006. Original Russian Text © M.V. Davidovich, 2006, published in Pis’ma v Zhurnal Tekhnicheskoœ Fiziki, 2006, Vol. 32, No. 22, pp. 53–63. 982 Any wave or oscillatory process can be character- ized by the electromagnetic energy density U and the energy transfer velocity v e . The latter quantity can be defined, based on the concept of Umov [1], in terms of the density U and the Poynting vector P(r, t) as [2–6] (1) This possibility follows from the law of energy conser- vation under conventional assumptions. In vacuum, the energy density can be written as In a medium, the energy density is also frequently described using an analogous expression [3–6] as (2) However, this expression can be used only for static fields at a constant temperature, since relations of the type D(r, t) = ε 0 εE(r, t) are not valid in the general case. In a static field at a constant temperature, the quantity defined by Eq. (2) coincides with the free energy den- sity [3, 7, 8]. In a medium, U implies the density of the internal energy in the field–substance system (so that, in the absence of fields, U = 0). The presence of tempo- ral dispersion implies an integral relation between the field and induction vectors [7–10] via the correspond- v e r t , ( ) Er t , ( ) Hr t , ( ) / U r t , ( ) × = = Pr t , ( ) / U r t , ( ) . U r t , ( ) U E U H + ε 0 E 2 r t , ( ) /2 μ 0 H 2 r t , ( ) /2. + = = U r t , ( ) U E r t , ( ) U H r t , ( ) + = = Er t , ( ) Dr t , ( ) /2 Hr t , ( ) Br t , ( ) /2. + ing permittivities: (3) The local conservation law [2–6] written as (4) where J in is the density of the field source power and ∂ t = ∂/∂t, implies that ∂ t W(r, t) = E(r, t)∂ t D(r, t) + H(r, t)∂ t B(r, t). The density of energy (work) W spent for the field generation can be described as Dr t , ( ) ε 0 ε ˆ Er t , ( ) ε 0 Er t , ( ) = = + ε 0 κ ˆ r t t' – , ( ) Er t' , ( ) t' d t 0 t ∫ = ε 0 ε ˆ r t t' – , ( ) Er t' , ( ) t'. d t 0 t ∫ J in r t , ( ) Er t , ( ) = ∂ t W r t , ( ) σ E 2 r t , ( ) ∇ Pr t , ( ) , ⋅ + + W r t , ( ) Er t' , ( ) ∂ ∂ t' ----- Dr t' , ( ) ⎩ ⎨ ⎧ t 0 t ∫ = + Hr t' , ( ) ∂ ∂ t' ----- Br t' , ( ) ⎭ ⎬ ⎫ dt' Er t , ( ) Dr t , ( ) = + Hr t , ( ) Br t , ( ) Dr t' , ( ) ∂ ∂ t' ----- Er t' , ( ) ⎩ ⎨ ⎧ t 0 t ∫ – Electromagnetic Energy Density and Velocity in a Medium with Anomalous Positive Dispersion M. V. Davidovich Saratov State University, Saratov, 419026 Russia e-mail: DavidivichMV@info.sgu.ru Received March 21, 2006 Abstract—The simple laws of dispersion, the electromagnetic energy density, and the phase, group, and energy transfer velocities in dissipative media are considered. In polar dielectrics with an anomalous positive disper- sion described by the Debye formula, the energy transfer velocity in a plane monochromatic wave coincides with the phase velocity, while the group velocity can exceed the speed of light. PACS numbers: 03.50.Kk DOI: 10.1134/S106378500611023X