Electromagnetics

Content: 1 Introductory concepts1.1 Notation, conventions, and symbology1.2 The field concept of electromagnetics1.3 The sources of the electromagnetic field1.4 Problems2 Maxwell's theory of electromagnetism2.1 The postulate2.2 The well-posed nature of the postulate 2.3 Maxwell's equations in moving frames2.4 The Maxwell-Boffi equations2.5 Large-scale form of Maxwell's equations2.6 The nature of the four field quantities2.7 Maxwell's equations with magnetic sources2.8 Boundary (jump) conditions2.9 Fundamental theorems 2.10 The wave nature of the electromagnetic field2.11 Application: single charged particle motion in static electric and magnetic fields2.12 Problems3 The static and quasistatic electromagnetic fields3.1 Statics and quasistatics3.2 Static fields and steady currents3.3 Electrostatics3.4 Magnetostatics3.5 Static field theorems3.6 Quasistatics 3.7 Application: electromagnetic shielding3.8 Problems4 Temporal and spatial frequency domain representation4.1 Interpretation of the temporal transform4.2 The frequency-domain Maxwell equations4.3 Boundary conditions on the frequency-domain fields4.4 The constitutive and Kramers-Kronig relations4.5 Dissipated and stored energy in a dispersive medium4.6 Some simple models for constitutive parameters4.7 Monochromatic fields and the phasor domain4.8 Poynting's theorem for time-harmonic fields4.9 The complex Poynting theorem4.10 Fundamental theorems for time-harmonic fields4.11 The wave nature of the time-harmonic EM field4.12 Interpretation of the spatial transform4.13 Spatial Fourier decomposition4.14 Periodic fields and Floquet's theorem4.15 Application: electromagnetic characterization of materials4.16 Problems5 Field decompositions and the EM potentials5.1 Spatial symmetry decompositions5.2 Solenoidal-lamellar decomposition and the electromagnetic potentials5.3 Transverse-longitudinal decomposition5.4 TE-TM decomposition5.5 Solenoidal-lamellar decomposition of solutions to the vector wave equation and the vector spherical wave functions5.6 Application: guided waves and transmission lines5.7 Problems6 Integral solutions of Maxwell's equations6.1 Vector Kirchhoff solution6.2 Fields in an unbounded medium6.3 Fields in a bounded, source-free region6.4 Application: antennas6.5 Problems7 Integral equations in electromagnetics7.1 A brief overview of integral equations7.2 Plane-wave reflection from an inhomogeneous region7.3 Solution to problems involving thin wires7.4 Solution to problems involving two-dimensional conductors7.5 Scattering by a penetrable cylinder7.6 Apertures in ground planes7.7 Application: electromagnetic shielding revisited7.8 ProblemsAppendix A Mathematical appendixA.1 Conservative Vector FieldsA.2 The Fourier transformA.3 Vector transport theoremsA.4 Dyadic analysisA.5 Boundary value problemsAppendix B Useful identitiesAppendix C Fourier transform pairsAppendix D Coordinate systemsAppendix E Properties of special functionsE.1 Bessel functionsE.2 Legendre functionsE.3 Spherical harmonicsAppendix F Derivation of an integral identity