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Tables of Contents for Intermediate Electromagnetic Theory
Chapter/Section Title
Page #
Page Count
Preface
v
The Mathematics of Electricity and Magnetism
1
49
Scalars, Vectors and Vector Addition
1
3
Vector Multiplication
4
6
Fields
10
1
Vector Calculus: The Gradient
11
5
The Divergence of a Vector
16
1
The Divergence Theorem
17
4
The Curl of a Vector
21
1
Stokes's Theorem
22
3
Derivatives of Scalar and Vector Products
25
1
Higher Derivatives
25
2
Curvilinear Coordinates
27
8
Tensors and Matrices
35
9
Complex Numbers
44
6
Appendix I: Vector Identities
47
2
References
49
1
Electrostatics
50
61
Coulomb's Law
51
3
The Principle of Superposition; Charge Distribution
54
3
The Electric Field
57
2
Calculation of the Electric Field
59
7
Conductors and Insulators
66
2
Gauss's Law
68
12
The Electric Potential
80
5
Calculation of the Electric Potential
85
6
The Continuity Equations for E and Φ
91
2
Capacitors
93
3
The Equations of Laplace and Poisson: The Second Derivatives of the Potential Field
96
1
The Dirac δ-Function
96
3
Electrostatic Energy
99
12
Appendix II: The Dirac δ-Function
105
3
Supplementary Problems
108
2
References
110
1
Boundary Value Problems: The Solutions to Laplace's Equation and Poisson's Equation
111
86
Boundary Conditions
111
1
The Superposition Theorem
112
1
The Uniqueness Theorem
112
1
Solution to Laplace's Equation in One or Two Dimensions: Cartesian Coordinates
113
6
Laplace's Equation in One and Two Dimensions; Cylindrical Symmetry
119
11
Laplace's Equation in One or Two Dimensions; Spherical Coordinates
130
10
The Solution to Laplace's Equation in Three Dimensions
140
4
Poisson's Equation
144
2
The Method of Images
146
7
Green's Functions; The General Solution of Poisson's Equation
153
44
Appendix III: Bessel Functions
167
1
III-1: Regular Bessel Functions
167
9
III-2: The Generating Function for the Bessel Functions
176
1
III-3: Modified Bessel Functions
177
3
Appendix IV: Legendre Polynomials
180
1
IV-1: The Legendre Polynomials
180
7
IV-2: The Generating Function for the Legendre Polynomials
187
1
IV-3: The Associated Legendre Polynomials
188
4
Supplementary Problems
192
3
References
195
2
Current and Conduction
197
34
Current and Current Density
197
2
Conductivity, Resistance and Ohms Law
199
5
Microscopic Description of Conductivity
204
5
The Band Theory of Solids
209
3
Conductivity in Metals
212
2
Fermi-Dirac Statistics; Conductivity in Semiconductors and Insulators
214
2
Doped Semiconductors
216
3
Conductivity in a P-N Junction
219
1
Properties of the P-N Junction
220
3
Conductivity in an Electron Gas
223
3
Superconductivity
226
1
The Josephson Effect
227
4
References
230
1
The Magnetic Field of Steady Currents
231
64
The Biot-Savart Law
232
12
The Divergence of B; Magnetic Flux
244
2
The Curl of B
246
2
Ampere's Law
248
11
The Magnetic Scalar Potential
259
4
The Magnetic Vector Potential
263
14
The Lorentz Force Law
277
9
The Hall Effect
286
9
Appendix V: Elliptic Integrals
290
4
References
294
1
The Electric Field in Matter
295
56
The Dipole Field
296
4
Energy, Force and Torque on a Dipole
300
1
The Electric Field Outside a Dielectric
301
2
The Electric Field Inside a Dielectric
303
3
Gauss's Law in a Dielectric; The Displacement Vector
306
2
Electric Susceptibility and the Dielectric Constant
308
6
Dielectric Materials
314
3
Derivation of Susceptibility from the Molecular Polarization
317
2
Boundary Conditions for Dielectric Surfaces
319
13
Electrostatic Energy in Dielectrics
332
1
Interaction of the Electric Field with a Plasma
333
2
The Multipole Expansion of a Charge Distribution
335
4
Expansion in Cartesian Coordinates
339
5
Expansion in Spherical Harmonics
344
7
Supplementary Problems
348
2
References
350
1
Magnetic Fields in Matter
351
36
Multipole Expansion of the Magnetic Field
351
3
Magnetic Fields in Magnetic Materials
354
3
Magnetic Fields Inside Matter
357
5
Boundary Conditions on the Magnetic Field Vectors
362
2
Boundary Value Problems of the Magnetic Field
364
3
The Nature of Magnetic Materials
367
6
Ferromagnetism
373
4
Other Magnetic Materials
377
1
The Temperature Dependence of Paramagnetism
378
3
Superconductivity
381
6
References
386
1
Time Dependent Fields; Faraday's Law
387
37
Faraday's Law
387
2
The Electromotive Force
389
2
Lenz's Law
391
1
Motional Electromotive Force
392
1
General Electromotive Force
393
5
The Differential Faraday's Law
398
7
The Time Dependent Field Potentials
405
1
Inductance
405
5
Self-Inductance
410
4
The Energy of the Magnetic Field
414
10
References
423
1
Maxwell's Equations
424
66
The Displacement Current
425
5
The Wave Equation
430
4
The Time-Dependent Potential Function
434
3
Poynting's Theorem
437
5
Field Momentum
442
4
Solution of the Wave Equation
446
2
Description of Waves in Complex Numbers
448
2
Parameters of the Wave Equation
450
3
Electromagnetic Waves
453
3
Polarization
456
3
General Description of a Plane Wave
459
2
Energy of a Wave
461
4
Spherical Waves
465
25
Appendix VI: Units
473
1
VI-1: Base Units
474
2
VI-2: SI Prefixes
476
1
VI-3: Derived Units
477
1
VI-4: Measurement Standards
478
2
VI-5: Units in Electricity and Magnetism
480
9
References
489
1
Applications of Maxwell's Equations: The Optics of Plane Waves
490
77
The Laws of Reflection and Refraction
490
6
The Amplitudes of the Reflected and Transmitted Waves: Fresnel's Equations
496
10
Total Internal Reflection
506
7
Interaction of Plane Electromagnetic Waves with Conductors
513
14
Interference
527
13
Diffraction
540
15
Optical Dispersion
555
12
Supplementary Problems
565
1
References
566
1
Application of Maxwell's Equations: Guided Waves
567
56
The Rectangular Metal Waveguide
567
20
The Circular Cylindrical Waveguide
587
10
The Coaxial Waveguide
597
3
Cavity Resonators
600
4
Attenuation in Waveguides
604
5
Dielectric Waveguides
609
14
References
622
1
Application of Maxwell's Equations: Radiation
623
58
Solution of the Inhomogeneous Wave Equation
623
3
Multipole Expansion of a Time Dependent Charge Distribution
626
3
The Field of an Electric Dipole
629
12
Antenna Radiation --- The Center Fed Antenna
641
4
The Half-Wave Antenna
645
3
Antenna Arrays
648
2
The Hertz Vector Potentials
650
4
The Radiation Field of Moving Particles
654
17
Radiation Reaction
671
10
Appendix VII: Fourier Integrals: General Solution to the Inhomogeneous Wave Equation
674
6
References
680
1
Relativity
681
58
The Galilean Transformation
681
2
The Electromagnetic Test of Relativity
683
2
The Trouton-Noble Experiment
685
2
The Michelson Morley Experiment
687
4
The Postulates of Einstein
691
7
The Lorentz Transformation
698
6
The Effect of the Lorentz Transformation
704
7
The Tensor Formulation of Relativity
711
3
The Transformation of Velocity and Momentum
714
5
The Covariant Formulation of the Electromagnetic Field
719
6
The Maxwell Stress Tensor
725
3
The Field of a Uniformly Moving Charge
728
4
The Relativistic Derivation of the Radiation Fields
732
2
The Relativistic Motion of Charged Particles in an Electromagnetic Field; The Relativistic Lorentz Force Law
734
5
References
738
1
Index
739