3. 4.1 Mean value theorem of electrostatics 3.4.2 Earnshaw's theorem 3. 4.3 Thomson's theorem 3.4.4 Greens reciprocation theorem 3.5 Problems Temporal and spatial frequency domain representation 4.1 Interpretation of the temporal transform 4.2 The frequency-domain Maxwell equations 4.3 Boundary conditions on the frequency-domain fields 4.4 The constitutive and Kronig-Kramers relations 4.4.1 The complex permittivit 4.4.2 High and low frequency behavior of constitutive parameters 4.4.3 The Kronig-Kramers relations 5 Dissipated and stored energy in a dispersive medium 4.5.1 Dissipation in a dispersive material 4.5.2 Energy stored in a dispersive material 4.5.3 The energy theorem 4.6 Some simple models for constitutive parameters 4.6.1 Complex permittivity of a non-magnetized plasma 4.6.2 Complex dyadic permittivity of a magnetized plasma 4.6.3 Simple models of dielectrics 4.6.4 Permittivity and conductivity of a conducto 4.6.5 Permeability dyadic of a ferrite 4.7 Monochromatic fields and the phasor domain 4.7.1 The time-harmonic em fields and constitutive relations 4.7.2 The phasor fields and Maxwells equations 4.7.3 Boundary conditions on the phasor fields 4.8 Poynting's theorem for time-harmonic fields 4.8.1 General form of Poynting's theorem 4.8.2 Poynting's theorem for nondispersive materials 4.8.3 Lossless, lossy, and active media 4.9 The complex Poynting theorem 4.9.1 Boundary condition for the time-average Poynting vector 4.10 Fundamental theorems for time-harmonic fields 4.10.1 Uniqueness 4. 10.2 Reciprocity revisited 4.10.3 Duality 4.11 The wave nature of the time-harmonic em field 4. 11.1 The frequency-domain wave equation 11.2 Field relationships and the wave equation for two-dimensional fields 4. 11.3 Plane waves in a homogeneous, isotropic, lossy material 4. 11.4 Monochromatic plane waves in a lossy medium 4. 11.5 Plane waves in layered media 4. 11.6 Plane-wave propagation in an anisotropic ferrite medium 4. 11.7 Propagation of cylindrical waves 4. 11.8 Propagation of spherical waves in a conducting medium 4.11.9 Nonradiating sources 0 2001 by CRC Press LLC3.4.1 Mean value theorem of electrostatics 3.4.2 Earnshaw’s theorem 3.4.3 Thomson’s theorem 3.4.4 Green’s reciprocation theorem 3.5 Problems 4 Temporal and spatial frequency domain representation 4.1 Interpretation of the temporal transform 4.2 The frequency-domain Maxwell equations 4.3 Boundary conditions on the frequency-domain fields 4.4 The constitutive and Kronig–Kramers relations 4.4.1 The complex permittivity 4.4.2 High and low frequency behavior of constitutive parameters 4.4.3 The Kronig–Kramers relations 4.5 Dissipated and stored energy in a dispersive medium 4.5.1 Dissipation in a dispersive material 4.5.2 Energy stored in a dispersive material 4.5.3 The energy theorem 4.6 Some simple models for constitutive parameters 4.6.1 Complex permittivity of a non-magnetized plasma 4.6.2 Complex dyadic permittivity of a magnetized plasma 4.6.3 Simple models of dielectrics 4.6.4 Permittivity and conductivity of a conductor 4.6.5 Permeability dyadic of a ferrite 4.7 Monochromatic fields and the phasor domain 4.7.1 The time-harmonic EM fields and constitutive relations 4.7.2 The phasor fields and Maxwell’s equations 4.7.3 Boundary conditions on the phasor fields 4.8 Poynting’s theorem for time-harmonic fields 4.8.1 General form of Poynting’s theorem 4.8.2 Poynting’s theorem for nondispersive materials 4.8.3 Lossless, lossy, and active media 4.9 The complex Poynting theorem 4.9.1 Boundary condition for the time-average Poynting vector 4.10 Fundamental theorems for time-harmonic fields 4.10.1 Uniqueness 4.10.2 Reciprocity revisited 4.10.3 Duality 4.11 The wave nature of the time-harmonic EM field 4.11.1 The frequency-domain wave equation 4.11.2 Field relationships and the wave equation for two-dimensional fields 4.11.3 Plane waves in a homogeneous, isotropic, lossy material 4.11.4 Monochromatic plane waves in a lossy medium 4.11.5 Plane waves in layered media 4.11.6 Plane-wave propagation in an anisotropic ferrite medium 4.11.7 Propagation of cylindrical waves 4.11.8 Propagation of spherical waves in a conducting medium 4.11.9 Nonradiating sources