Textbook
The Power and Beauty of Electromagnetic FieldsISBN: 9781118057575
678 pages
October 2011, ©2011, WileyIEEE Press

Description
Unique, multilevel textbook is adaptable to introductory, intermediate, and advanced levels
This revolutionary textbook takes a unique approach to electromagnetic theory, comparing both conventional and modern theories. It explores both the MaxwellPoynting representation as well as the Alternate representation, which the author demonstrates is generally simpler and more suitable for analyzing modern electromagnetic environments. Throughout the text, students and researchers have the opportunity to examine both of these theories and discover how each one can be applied to solve problems.
The text is divided into four parts:

Part I: Basic Electromagnetic Theory includes Maxwell's equations, quasistatics, power and energy, stress and momentum, and electromagnetic wave theorems and principles

Part II: FourDimensional Electromagnetism includes fourdimensional vectors and tensors and energymomentum tensors

Part III: Electromagnetic Examples includes statics and quasistatics, accelerating charges, plane waves, transmission lines, waveguides, antennas and diffraction, and ferrites

Part IV: Backmatter includes a summary, appendices, and references
Designed to accommodate a broad range of interests and backgrounds, the text's companion DVD enables readers to reconfigure the material as an introductory, intermediate, or advancedlevel text. Moreover, the text and its DVD offer a broad range of features that make it possible for readers to quickly grasp new concepts and apply them in practice:

Practice problems provide the opportunity to solve realworld problems using electromagnetic theory

Forty animations illustrate electric and magnetic field transients

Line drawings and computergenerated mathematical figures clarify complex concepts and procedures.

Maxima, a powerful symbolic mathematics program, helps readers explore fourdimensional electromagnetic theory as well as perform numerical and graphical analyses
Adaptable to multiple levels, this text can be used for both undergraduate and graduate coursework. It is also recommended as a reference for researchers in such fields as electrical engineering, laser physics, materials science, and biomedical engineering.
Table of Contents
Acknowledgments xxvii
List of Figures xxix
PART I BASIC ELECTROMAGNETIC THEORY
1 Maxwell’s Equations 5
1.1 Mathematical notation 5
1.2 Freespace 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 FreeSpace 61
4.1 Homogeneous waves 61
4.2 Onedimensional 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 FOURDIMENSIONAL ELECTROMAGNETISM
7 FourDimensional Vectors and Tensors 105
7.1 Space–time coordinates 105
7.2 Fourvector electriccurrent density 106
7.3 Fourvector potential (Lorenz gauge) 106
7.4 FourLaplacian (wave equation) 107
7.5 Maxwell’s Equations and field tensors 107
7.6 The fourdimensional curl operator 109
7.7 Fourdimensional “statics” 110
7.8 Fourdimensional force density 112
7.9 Sixvectors and dual field tensors 113
7.10 Fourvector electric and magnetic fields 113
7.11 The field tensors and Maxwell’s Equations revisited 115
7.12 Linear conductors revisited 116
8 EnergyMomentum Tensors 119
8.1 Introduction 119
8.2 Maxwell–Poynting energymomentum tensor 121
8.3 Alternate energymomentum 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 energymomentum 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 Energymomentum tensors and fourforce 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 Resistivesheet 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 Dopplershifted TEM plane waves 257
16.3 Nonuniform plane waves 258
16.4 Skindepthlimited 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 timedependent solutions 271
18.2 Parallelplate TEM line in the sinusoidal steady state 274
18.3 TEM taperedplate “horn” transformer 280
18.4 TEM line with parallel plates of high conductivity 282
18.5 Parallelplate 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 Alternatepower and Alternateenergy 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 Halfwave dipoles 342
22.3 Selfcomplementary planar antennas 345
22.4 Travelingwave 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 Largesignal equations 380
23.4 Linearized (smallsignal) equations 381
23.5 Uniform precession in a small ellipsoid 383
23.6 Plane wave solutions 384
23.7 Smallsignal power and energy 388
23.8 Smallsignal 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 Fourdimensional 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 Threedimensional vector identities and theorems 538
B.3 Fourdimensional vector and tensor identities 543
B.4 Fourspace 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 Stressmomentum 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 linecurrent transients 622
H.5 Animated field of a radiating Hertzian dipole 623
H.6 Animated beautypower fluxes of cylindrical waveguide modes 623
H.7 Macsyma animations and graphics 624
References 627
Index 631
Author Information
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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