Power and Beauty of Electromagnetic Fields

Frederic R. Morgenthaler, PhD, joined the faculty of the Massachusetts Institute of Technology in 1960, becoming a Full Professor in 1968. He retired from MIT in 1996 and is currently Professor Emeritus of Electrical Engineering. Dr. Morgenthaler has served as a consultant to the U.S. government as well as private industry. A Fellow of the IEEE and the holder of approximately one dozen patents, Dr. Morgenthaler has authored over 100 scientific publications and papers.

• Preface xxi Acknowledgments xxviiList of Figures xxixPART I BASIC ELECTROMAGNETIC THEORY1 Maxwell’s Equations 51.1 Mathematical notation 51.2 Free-space fields and forces 61.3 Vector and scalar potentials 101.4 Inhomogeneous wave equations for E and H 121.5 Static fields 121.6 Integration of the inhomogeneous wave equation 151.7 Polarizable, magnetizable, and conducting media 181.8 Boundary conditions 241.9 The complex Maxwell Equations 262 Quasistatic Approximations 292.1 Quasistatic expansions of a standing wave 302.2 Electroquasistatic (EQS) fields 312.3 Magnetoquasistatic (MQS) fields 332.4 Conduction problems 352.5 Laplacian approximations 373 Electromagnetic Power, Energy, Stress, and Momentum 393.1 Introduction 393.2 The Maxwell–Poynting representation 413.3 Quasistatic power and energy 433.4 Alternative representations 453.5 Differences between representations 544 Electromagnetic Waves in Free-Space 614.1 Homogeneous waves 614.2 One-dimensional waves 624.3 Harmonic uniform plane waves 634.4 Waves of high symmetry 644.5 Inhomogeneous scalar wave equations 665 Electromagnetic Waves in Linear Materials 675.1 Introduction 675.2 Electrically conducting media 675.3 Linear dielectric and magnetic media 706 Electromagnetic Theorems and Principles 776.1 Introduction 776.2 Complex power and energy theorems 786.3 Complex stress theorems 846.4 Complex momentum theorems 866.5 Duality 886.6 Uniqueness theorems 946.7 The equivalence principle 966.8 The induction theorem 976.9 Babinet’s Principle 986.10 The reciprocity theorem 100PART II FOUR-DIMENSIONAL ELECTROMAGNETISM7 Four-Dimensional Vectors and Tensors 1057.1 Space–time coordinates 1057.2 Four-vector electric-current density 1067.3 Four-vector potential (Lorenz gauge) 1067.4 Four-Laplacian (wave equation) 1077.5 Maxwell’s Equations and field tensors 1077.6 The four-dimensional curl operator 1097.7 Four-dimensional “statics” 1107.8 Four-dimensional force density 1127.9 Six-vectors and dual field tensors 1137.10 Four-vector electric and magnetic fields 1137.11 The field tensors and Maxwell’s Equations revisited 1157.12 Linear conductors revisited 1168 Energy-Momentum Tensors 1198.1 Introduction 1198.2 Maxwell–Poynting energy-momentum tensor 1218.3 Alternate energy-momentum tensors 1218.4 Boundary conditions and gauge considerations 1258.5 Electromagnetic beauty revisited 1269 Dielectric and Magnetic Materials 1299.1 Introduction 1299.2 Maxwell’s Equations with polarization and magnetization 1309.3 Amperian energy-momentum tensors 13110 Amperian, Minkowski, and Chu Formulations 14110.1 Introduction 14110.2 Maxwell’s Equations in the Amperian formulation 14110.3 Maxwell’s Equations in the Minkowski formulation 14210.4 Maxwell’s Equations in the Chu formulation 14310.5 Energy-momentum tensors and four-force densities 14510.6 Discussion of force densities 14810.7 The principle of virtual power 150PART III ELECTROMAGNETIC EXAMPLES11 Static and Quasistatic Fields 15711.1 Spherical charge distribution 15711.2 Electric field in a rectangular slot 15811.3 Current in a cylindrical conductor 16011.4 Sphere with uniform conductivity 16311.5 Quasistatic analysis of a physical resistor 17011.6 Magnetic diffusion 17912 Uniformly Moving Electric Charges 18312.1 Point charge 18312.2 Surface charges separating at constant velocity 18512.3 Expanding cylindrical surface charge 19012.4 Expanding spherical surface charge 19213 Accelerating Charges 19513.1 Hertzian electric dipole 19513.2 Hertzian magnetic dipole 20013.3 Radiation from an accelerated then decelerated charge 20214 Uniform Surface Current 20714.1 Pulse excitations 20714.2 Resistive-sheet detector 21414.3 Additional pulse waveforms 21715 Uniform Line Currents 22315.1 Axial current step (integral laws) 22315.2 Axial current step (differential laws) 23715.3 Superposition of axial line currents 24015.4 Axial current with multiple pulses 24615.5 Fields of a sinusoidal axial current 25116 Plane Waves 25516.1 Uniform TEM plane waves 25516.2 Doppler-shifted TEM plane waves 25716.3 Nonuniform plane waves 25816.4 Skin-depth-limited current in a conductor 26117 Waves Incident at a Material Interface 26317.1 Reflected and transmitted plane waves 26317.2 TE polarization 26417.3 TM polarization 26717.4 Elliptically polarized incident waves 26918 TEM Transmission Lines 27118.1 General time-dependent solutions 27118.2 Parallel-plate TEM line in the sinusoidal steady state 27418.3 TEM tapered-plate “horn” transformer 28018.4 TEM line with parallel plates of high conductivity 28218.5 Parallel-plate TEM line loaded with linear material 28919 Rectangular Waveguide Modes 29319.1 Introduction 29319.2 Periodic potentials and fields 29419.3 Waveguide dispersion 29519.4 TEnm modes 29619.5 TMnm modes 29819.6 Null Alternate-power and Alternate-energy distributions 29919.7 Uniqueness resolved 30020 Circular Waveguide Modes 30520.1 Introduction 30520.2 TMnm modes 30720.3 TEnm modes 31020.4 Null Alternate power and energy distributions 32320.5 Alternate energy momentum and photons 32321 Dielectric Waveguides 33521.1 Introduction 33521.2 Symmetric TE modes 33621.3 Antisymmetric TE modes 33621.4 Dispersion relations 33722 Antennas and Diffraction 34122.1 Introduction 34122.2 Half-wave dipoles 34222.3 Self-complementary planar antennas 34522.4 Traveling-wave wire antennas 34522.5 The theory of simple arrays 34922.6 Diffraction by a rectangular slit 35622.7 Diffraction by a large circular aperture 36022.8 Diffraction by a small circular aperture 36922.9 Diffraction by the complementary screen 37122.10 Paraxial wave equation 37223 Waves and Resonances in Ferrites 37723.1 Introduction 37723.2 Ferrites 37823.3 Large-signal equations 38023.4 Linearized (small-signal) equations 38123.5 Uniform precession in a small ellipsoid 38323.6 Plane wave solutions 38423.7 Small-signal power and energy 38823.8 Small-signal stress and momentum 39123.9 Quasiparticle interpretation (magnons) 39324 Equivalent Circuits 39524.1 Receiving circuit of a dipole 39524.2 TEM transmission lines 39824.3 Lossless tapered lines 40624.4 Transients on transmission lines 40824.5 Plane waves (oblique incidence) 41124.6 Waveguides 41324.7 The scattering matrix 41824.8 Directional couplers 42124.9 Resonators 42125 Practice Problems 43525.1 Statics 43525.2 Quasistatics 44825.3 Plane waves 45825.4 Radiation and diffraction 46225.5 Transmission lines 47225.6 Waveguides 48125.7 Junctions and couplers 48525.8 Resonators 49025.9 Ferrites 49125.10 Four-dimensional electromagnetics 496PART IV BACKMATTERSummary 505Electromagnetic Luminaries 511About the Author 519Appendix A 521A.1 Theory of Special Relativity 521A.2 Transformations between fixed and moving coordinates 530Appendix B 537B.1 The unit step and uk (t ) functions 537B.2 Three-dimensional vector identities and theorems 538B.3 Four-dimensional vector and tensor identities 543B.4 Four-space identities 544Appendix C 547C.1 Stationary spatially symmetric sources 547C.2 Multipole expansions of static fields 550C.3 Averaging property of Laplace’s Equation 553C.4 Solutions of Laplace’s Equation 554C.5 Laplace’s Equation in N dimensions 558C.6 Ellipsoids in uniform fields 559Appendix D 563D.1 Alternate power, energy, stress, and momentum 563D.2 Minkowski representations 568D.3 Stress-momentum representations of torque 571Appendix E 577E.1 Fields of specified charges and currents 577E.2 Fields of a moving point charge 578E.3 Method of images 583E.4 Characteristic impedances of TEM transmission lines 586Appendix F 593F.1 Bessel functions 593F.2 Chebyshev polynomials 598F.3 Hermite polynomials 600Appendix G 601G.1 Macsyma and Maxima 601G.2 Macsyma program descriptions 602G.3 Macsyma notebooks 605G.4 Text of Macsyma/Maxima batch program 608Appendix H 619H.1 Animated fields of surface currents 619H.2 Animated fields of a cylindrical volume current, Jz (t ) = Jou−1(t ) 620H.3 Animated fields of a cylindrical surface current, Kz (t ) = Kou−1(t ) 621H.4 Animated fields of line-current transients 622H.5 Animated field of a radiating Hertzian dipole 623H.6 Animated beauty-power fluxes of cylindrical waveguide modes 623H.7 Macsyma animations and graphics 624References 627Index 631