Electromagnetic Fields, Second Edition

Electromagnetic Fields......Page 4
Contents......Page 10
Preface......Page 16
1. Linear Analysis......Page 18
1.1 Linear Spaces......Page 19
1.2 Linear Transformations......Page 22
1.3 The Inversion Problem......Page 25
1.4 Green’s Functions......Page 28
1.5 Reciprocity......Page 31
1.6 Green’s Dyadics......Page 34
1.7 Convergence of a Series......Page 36
1.8 Eigenfunctions......Page 37
1.9 Integral Operators......Page 40
1.10 Eigenfunction Expansions......Page 43
1.11 Discretization......Page 47
1.12 Matrices......Page 50
1.13 Solution of Matrix Equations: Stability......Page 53
1.14 Finite Differences......Page 55
1.15 Perturbations......Page 60
2. Variational Techniques......Page 68
2.1 Stationary functionals......Page 69
2.2 A Suitable Functional for the String Problem......Page 70
2.3 Functionals for the General L Transformation......Page 72
2.4 Euler’s Equations of Some Important Functionals......Page 75
2.5 Discretization of the Trial Functions......Page 77
2.6 Simple Finite Elements for Planar Problems......Page 79
2.7 More Finite Elements......Page 82
2.8 Direct Numerical Solution of Matrix Problems......Page 86
2.9 Iterative Numerical Solution of Matrix Problems......Page 87
3.1 Volume Charges in Vacuum......Page 94
3.2 Green’s Function for Infinite Space......Page 97
3.3 Multipole Expansion......Page 100
3.4 Potential Generated by a Single Layer of Charge......Page 103
3.5 Potential Generated by a Double Layer of Charge......Page 108
3.6 Potential Generated by a Linear Charge......Page 111
3.7 Spherical Harmonics......Page 115
3.8 Dielectric Materials......Page 119
3.9 Cavity Fields......Page 122
3.10 Dielectric Sphere in an External Field......Page 125
3.11 Dielectric Spheroid in an Incident Field......Page 128
3.12 Numerical Methods......Page 132
4.1 Conductivity......Page 142
4.2 Potential Outside a Charged Conductor......Page 144
4.3 Capacitance Matrix......Page 150
4.4 The Dirichlet Problem......Page 151
4.5 The Neumann Problem......Page 154
4.6 Numerical Solution of the Charge Density Problem......Page 156
4.7 Conductor in an External Field......Page 159
4.8 Conductors in the Presence of Dielectrics......Page 163
4.9 Current Injection into a Conducting Volume......Page 165
4.10 Contact Electrodes......Page 170
4.11 Chains of Conductors......Page 175
5.1 Two-Dimensional Potentials in the Plane......Page 184
5.2 Field Behavior at a Conducting Wedge......Page 188
5.3 Field Behavior at a Dielectric Wedge......Page 192
5.4 Separation of Variables in Two Dimensions......Page 194
5.5 Two-Dimensional Integral Equations......Page 198
5.6 Finite Methods in Two Dimensions......Page 202
5.7 Infinite Computational Domains......Page 205
5.8 More Two-Dimensional Techniques......Page 209
5.9 Layered Media......Page 213
5.10 Apertures......Page 216
5.11 Axisymmetric Geometries......Page 220
5.12 Conical Boundaries......Page 224
6.1 Magnetic Fields in Free Space: Vector Potential......Page 238
6.2 Fields Generated by Linear Currents......Page 241
6.3 Fields Generated by Surface Currents......Page 244
6.4 Fields at Large Distances from the Sources......Page 246
6.5 Scalar Potential in Vacuum......Page 249
6.6 Magnetic Materials......Page 251
6.7 Permanent Magnets......Page 253
6.8 The Limit of Infinite Permeability......Page 256
6.9 Two-Dimensional Fields in the Plane......Page 261
6.10 Axisymmetric Geometries......Page 266
6.11 Numerical Methods: Integral Equations......Page 268
6.12 Numerical Methods: Finite Elements......Page 270
6.13 Nonlinear Materials......Page 275
6.14 Strong Magnetic Fields and Force-Free Currents......Page 277
7.1 Maxwell’s Equations......Page 294
7.2 The Wave Equation......Page 297
7.3 Potentials......Page 299
7.4 Sinusoidal Time Dependence: Polarization......Page 303
7.5 Partially Polarized Fields......Page 307
7.6 The Radiation Condition......Page 310
7.7 Time-Harmonic Potentials......Page 313
7.8 Radiation Patterns......Page 317
7.9 Green’s Dyadics......Page 320
7.10 Multipole Expansion......Page 324
7.11 Spherical Harmonics......Page 330
7.12 Equivalent Sources......Page 337
7.13 Linear Wire Antennas......Page 344
7.14 Curved Wire Antennas: Radiation......Page 350
7.15 Transient Sources......Page 354
8.1 Constitutive Equations......Page 374
8.2 Plane Waves......Page 387
8.3 Ray Methods......Page 394
8.4 Beamlike Propagation......Page 405
8.5 Green’s Dyadics......Page 409
8.6 Reciprocity......Page 414
8.7 Equivalent Circuit of an Antenna......Page 419
8.8 Effective Antenna Area......Page 426
9.1 Plane Wave Incident on a Plane Boundary......Page 440
9.2 Propagation Through a Layered Medium......Page 459
9.3 The Sommerfeld Dipole Problem......Page 465
9.4 Multilayered Structures......Page 469
9.5 Periodic Structures......Page 477
9.6 Field Penetration Through Apertures......Page 495
9.7 Edge Diffraction......Page 507
10.1 Eigenvectors for an Enclosed Volume......Page 526
10.2 Excitation of a Cavity......Page 531
10.3 Determination of the Eigenvectors......Page 534
10.4 Resonances......Page 542
10.5 Open Resonators: Dielectric Resonances......Page 546
10.6 Aperture Coupling......Page 557
10.7 Green’s Dyadics......Page 561
11.1 The Scattering Matrix......Page 580
11.2 Cross Sections......Page 585
11.3 Scattering by a Sphere......Page 591
11.4 Resonant Scattering......Page 599
11.5 The Singularity Expansion Method......Page 603
11.6 Impedance Boundary Conditions......Page 615
11.7 Thin Layers......Page 618
11.8 Characteristic Modes......Page 621
12.1 The Electric Field Integral Equation......Page 634
12.2 The Magnetic Field Integral Equation......Page 641
12.3 The T-Matrix......Page 646
12.4 Numerical Procedures......Page 650
12.5 Integral Equations for Penetrable Bodies......Page 656
12.6 Absorbing Boundary Conditions......Page 663
12.7 Finite Elements......Page 668
12.8 Finite Differences in the Time Domain......Page 671
13.1 Physical Optics......Page 688
13.2 Geometrical Optics......Page 693
13.3 Geometric Theory of Diffraction......Page 698
13.4 Edge Currents and Equivalent Currents......Page 706
13.5 Hybrid Methods......Page 709
13.6 Low-Frequency Fields: The Rayleigh Region......Page 712
13.7 Non-Conducting Scatterers at Low Frequencies......Page 713
13.8 Perfectly Conducting Scatterers at Low Frequencies......Page 716
13.9 Good Conductors......Page 724
13.10 Stevenson’s Method Applied to Good Conductors......Page 728
13.11 Circuit Parameters......Page 732
13.12 Transient Eddy Currents......Page 736
14.1 E and H Waves......Page 750
14.2 Scattering by Perfectly Conducting Cylinders......Page 755
14.3 Scattering by Penetrable Circular Cylinders......Page 760
14.4 Scattering by Elliptic Cylinders......Page 763
14.5 Scattering by Wedges......Page 766
14.6 Integral Equations for Perfectly Conducting Cylinders......Page 768
14.7 Scattering by Penetrable Cylinders......Page 776
14.8 Low-Frequency Scattering by Cylinders......Page 781
14.9 Slots in a Planar Screen......Page 787
14.10 More Slot Couplings......Page 795
14.11 Termination of a Truncated Domain......Page 803
14.12 Line Methods......Page 809
15. Cylindrical Waveguides......Page 830
15.1 Field Expansions in a Closed Waveguide......Page 831
15.2 Determination of the Eigenvectors......Page 835
15.3 Propagation in a Closed Waveguide......Page 839
15.4 Waveguide Losses......Page 849
15.5 Waveguide Networks......Page 854
15.6 Aperture Excitation and Coupling......Page 860
15.7 Guided Waves in General Media......Page 876
15.8 Orthogonality and Normalization......Page 882
15.9 Dielectric Waveguides......Page 890
15.10 Other Examples of Waveguides......Page 899
16.1 Field Expansions for Axisymmetric Geometries......Page 922
16.2 Scattering by Bodies of Revolution: Integral Equations......Page 925
16.3 Scattering by Bodies of Revolution: Finite Methods......Page 929
16.4 Apertures in Axisymmetric Surfaces......Page 932
16.5 The Conical Waveguide......Page 935
16.6 Singularities at the Tip of a Cone......Page 943
16.7 Radiation and Scattering from Cones......Page 947
17.1 Fields Generated by a Moving Charge......Page 960
17.2 The Lorentz Transformation......Page 963
17.3 Transformation of Fields and Currents......Page 967
17.4 Radiation from Sources: the Doppler Effect......Page 972
17.5 Constitutive Equations and Boundary Conditions......Page 975
17.6 Material Bodies Moving Uniformly in Static Fields......Page 977
17.7 Magnetic Levitation......Page 979
17.8 Scatterers in Uniform Motion......Page 983
17.9 Material Bodies in Nonuniform Motion......Page 989
17.10 Rotating Bodies of Revolution......Page 991
17.11 Motional Eddy Currents......Page 996
17.12 Accelerated Frames of Reference......Page 1001
17.13 Rotating Comoving Frames......Page 1005
Appendix 1. Vector Analysis in Three Dimensions......Page 1018
Appendix 2. Vector Operators in Several Coordinate Systems......Page 1028
Appendix 3. Vector Analysis on a Surface......Page 1042
Appendix 4. Dyadic Analysis......Page 1052
Appendix 5. Special Functions......Page 1060
Appendix 6. Complex Integration......Page 1080
Appendix 7. Transforms......Page 1092
Appendix 8. Distributions......Page 1106
Appendix 9. Some Eigenfunctions and Eigenvectors......Page 1122
Appendix 10. Miscellaneous Data......Page 1128
General Texts on Electromagnetic Theory......Page 1134
Texts that Discuss Particular Areas of Electromagnetic Theory......Page 1135
General Mathematical Background......Page 1139
Mathematical Techniques Specifically Applied to Electromagnetic Theory......Page 1140
Acronyms and Symbols......Page 1144
Author Index......Page 1150
Subject Index......Page 1166