Preface xxi
Acknowledgments xxvii
List of Figures xxix
PART I BASIC ELECTROMAGNETIC THEORY
1 Maxwell’s Equations 5
1.1 Mathematical notation 5
1.2 Free-space fields and forces 6
1.3 Vector and scalar potentials 10
1.4 Inhomogeneous wave equations for E and H 12
1.5 Static fields 12
1.6 Integration of the inhomogeneous wave equation 15
1.7 Polarizable, magnetizable, and conducting media 18
1.8 Boundary conditions 24
1.9 The complex Maxwell Equations 26
2 Quasistatic Approximations 29
2.1 Quasistatic expansions of a standing wave 30
2.2 Electroquasistatic (EQS) fields 31
2.3 Magnetoquasistatic (MQS) fields 33
2.4 Conduction problems 35
2.5 Laplacian approximations 37
3 Electromagnetic Power, Energy, Stress, and Momentum 39
3.1 Introduction 39
3.2 The Maxwell–Poynting representation 41
3.3 Quasistatic power and energy 43
3.4 Alternative representations 45
3.5 Differences between representations 54
4 Electromagnetic Waves in Free-Space 61
4.1 Homogeneous waves 61
4.2 One-dimensional waves 62
4.3 Harmonic uniform plane waves 63
4.4 Waves of high symmetry 64
4.5 Inhomogeneous scalar wave equations 66
5 Electromagnetic Waves in Linear Materials 67
5.1 Introduction 67
5.2 Electrically conducting media 67
5.3 Linear dielectric and magnetic media 70
6 Electromagnetic Theorems and Principles 77
6.1 Introduction 77
6.2 Complex power and energy theorems 78
6.3 Complex stress theorems 84
6.4 Complex momentum theorems 86
6.5 Duality 88
6.6 Uniqueness theorems 94
6.7 The equivalence principle 96
6.8 The induction theorem 97
6.9 Babinet’s Principle 98
6.10 The reciprocity theorem 100
PART II FOUR-DIMENSIONAL ELECTROMAGNETISM
7 Four-Dimensional Vectors and Tensors 105
7.1 Space–time coordinates 105
7.2 Four-vector electric-current density 106
7.3 Four-vector potential (Lorenz gauge) 106
7.4 Four-Laplacian (wave equation) 107
7.5 Maxwell’s Equations and field tensors 107
7.6 The four-dimensional curl operator 109
7.7 Four-dimensional “statics” 110
7.8 Four-dimensional force density 112
7.9 Six-vectors and dual field tensors 113
7.10 Four-vector electric and magnetic fields 113
7.11 The field tensors and Maxwell’s Equations revisited 115
7.12 Linear conductors revisited 116
8 Energy-Momentum Tensors 119
8.1 Introduction 119
8.2 Maxwell–Poynting energy-momentum tensor 121
8.3 Alternate energy-momentum tensors 121
8.4 Boundary conditions and gauge considerations 125
8.5 Electromagnetic beauty revisited 126
9 Dielectric and Magnetic Materials 129
9.1 Introduction 129
9.2 Maxwell’s Equations with polarization and magnetization 130
9.3 Amperian energy-momentum tensors 131
10 Amperian, Minkowski, and Chu Formulations 141
10.1 Introduction 141
10.2 Maxwell’s Equations in the Amperian formulation 141
10.3 Maxwell’s Equations in the Minkowski formulation 142
10.4 Maxwell’s Equations in the Chu formulation 143
10.5 Energy-momentum tensors and four-force densities 145
10.6 Discussion of force densities 148
10.7 The principle of virtual power 150
PART III ELECTROMAGNETIC EXAMPLES
11 Static and Quasistatic Fields 157
11.1 Spherical charge distribution 157
11.2 Electric field in a rectangular slot 158
11.3 Current in a cylindrical conductor 160
11.4 Sphere with uniform conductivity 163
11.5 Quasistatic analysis of a physical resistor 170
11.6 Magnetic diffusion 179
12 Uniformly Moving Electric Charges 183
12.1 Point charge 183
12.2 Surface charges separating at constant velocity 185
12.3 Expanding cylindrical surface charge 190
12.4 Expanding spherical surface charge 192
13 Accelerating Charges 195
13.1 Hertzian electric dipole 195
13.2 Hertzian magnetic dipole 200
13.3 Radiation from an accelerated then decelerated charge 202
14 Uniform Surface Current 207
14.1 Pulse excitations 207
14.2 Resistive-sheet detector 214
14.3 Additional pulse waveforms 217
15 Uniform Line Currents 223
15.1 Axial current step (integral laws) 223
15.2 Axial current step (differential laws) 237
15.3 Superposition of axial line currents 240
15.4 Axial current with multiple pulses 246
15.5 Fields of a sinusoidal axial current 251
16 Plane Waves 255
16.1 Uniform TEM plane waves 255
16.2 Doppler-shifted TEM plane waves 257
16.3 Nonuniform plane waves 258
16.4 Skin-depth-limited current in a conductor 261
17 Waves Incident at a Material Interface 263
17.1 Reflected and transmitted plane waves 263
17.2 TE polarization 264
17.3 TM polarization 267
17.4 Elliptically polarized incident waves 269
18 TEM Transmission Lines 271
18.1 General time-dependent solutions 271
18.2 Parallel-plate TEM line in the sinusoidal steady state 274
18.3 TEM tapered-plate “horn” transformer 280
18.4 TEM line with parallel plates of high conductivity 282
18.5 Parallel-plate TEM line loaded with linear material 289
19 Rectangular Waveguide Modes 293
19.1 Introduction 293
19.2 Periodic potentials and fields 294
19.3 Waveguide dispersion 295
19.4 TEnm modes 296
19.5 TMnm modes 298
19.6 Null Alternate-power and Alternate-energy distributions 299
19.7 Uniqueness resolved 300
20 Circular Waveguide Modes 305
20.1 Introduction 305
20.2 TMnm modes 307
20.3 TEnm modes 310
20.4 Null Alternate power and energy distributions 323
20.5 Alternate energy momentum and photons 323
21 Dielectric Waveguides 335
21.1 Introduction 335
21.2 Symmetric TE modes 336
21.3 Antisymmetric TE modes 336
21.4 Dispersion relations 337
22 Antennas and Diffraction 341
22.1 Introduction 341
22.2 Half-wave dipoles 342
22.3 Self-complementary planar antennas 345
22.4 Traveling-wave wire antennas 345
22.5 The theory of simple arrays 349
22.6 Diffraction by a rectangular slit 356
22.7 Diffraction by a large circular aperture 360
22.8 Diffraction by a small circular aperture 369
22.9 Diffraction by the complementary screen 371
22.10 Paraxial wave equation 372
23 Waves and Resonances in Ferrites 377
23.1 Introduction 377
23.2 Ferrites 378
23.3 Large-signal equations 380
23.4 Linearized (small-signal) equations 381
23.5 Uniform precession in a small ellipsoid 383
23.6 Plane wave solutions 384
23.7 Small-signal power and energy 388
23.8 Small-signal stress and momentum 391
23.9 Quasiparticle interpretation (magnons) 393
24 Equivalent Circuits 395
24.1 Receiving circuit of a dipole 395
24.2 TEM transmission lines 398
24.3 Lossless tapered lines 406
24.4 Transients on transmission lines 408
24.5 Plane waves (oblique incidence) 411
24.6 Waveguides 413
24.7 The scattering matrix 418
24.8 Directional couplers 421
24.9 Resonators 421
25 Practice Problems 435
25.1 Statics 435
25.2 Quasistatics 448
25.3 Plane waves 458
25.4 Radiation and diffraction 462
25.5 Transmission lines 472
25.6 Waveguides 481
25.7 Junctions and couplers 485
25.8 Resonators 490
25.9 Ferrites 491
25.10 Four-dimensional electromagnetics 496
PART IV BACKMATTER
Summary 505
Electromagnetic Luminaries 511
About the Author 519
Appendix A 521
A.1 Theory of Special Relativity 521
A.2 Transformations between fixed and moving coordinates 530
Appendix B 537
B.1 The unit step and uk (t ) functions 537
B.2 Three-dimensional vector identities and theorems 538
B.3 Four-dimensional vector and tensor identities 543
B.4 Four-space identities 544
Appendix C 547
C.1 Stationary spatially symmetric sources 547
C.2 Multipole expansions of static fields 550
C.3 Averaging property of Laplace’s Equation 553
C.4 Solutions of Laplace’s Equation 554
C.5 Laplace’s Equation in N dimensions 558
C.6 Ellipsoids in uniform fields 559
Appendix D 563
D.1 Alternate power, energy, stress, and momentum 563
D.2 Minkowski representations 568
D.3 Stress-momentum representations of torque 571
Appendix E 577
E.1 Fields of specified charges and currents 577
E.2 Fields of a moving point charge 578
E.3 Method of images 583
E.4 Characteristic impedances of TEM transmission lines 586
Appendix F 593
F.1 Bessel functions 593
F.2 Chebyshev polynomials 598
F.3 Hermite polynomials 600
Appendix G 601
G.1 Macsyma and Maxima 601
G.2 Macsyma program descriptions 602
G.3 Macsyma notebooks 605
G.4 Text of Macsyma/Maxima batch program 608
Appendix H 619
H.1 Animated fields of surface currents 619
H.2 Animated fields of a cylindrical volume current, Jz (t ) = Jou−1(t ) 620
H.3 Animated fields of a cylindrical surface current, Kz (t ) = Kou−1(t ) 621
H.4 Animated fields of line-current transients 622
H.5 Animated field of a radiating Hertzian dipole 623
H.6 Animated beauty-power fluxes of cylindrical waveguide modes 623
H.7 Macsyma animations and graphics 624
References 627
Index 631
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.
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