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Tables of Contents for Classical Electrodynamics
Chapter/Section Title
Page #
Page Count
Introduction and Survey
1
23
1.1 Maxwell Equations in Vacuum, Fields, and Sources
2
3
1.2 Inverse Square Law, or the Mass of the Photon
5
4
1.3 Linear Superposition
9
4
1.4 Maxwell Equations in Macroscopic Media
13
3
1.5 Boundary Conditions at Interfaces Between Different Media
16
3
1.6 Some Remarks on Idealizations in Electromagnetism
19
3
References and Suggested Reading
22
2
Chapter 1 Introduction to Electrostatics
24
33
1.1 Coulomb's Law
24
1
1.2 Electric Field
24
3
1.3 Gauss's Law
27
1
1.4 Differential Form of Gauss's Law
28
1
1.5 Another Equation of Electrostatics and the Scalar Potential
29
2
1.6 Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential
31
3
1.7 Poisson and Laplace Equations
34
1
1.8 Green's Theorem
35
2
1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions
37
1
1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function
38
2
1.11 Electrostatic Potential Energy and Energy Density; Capacitance
40
3
1.12 Variational Approach to the Solution of the Laplace and Poisson Equations
43
4
1.13 Relaxation Method for Two-Dimensional Electrostatic Problems
47
3
References and Suggested Reading
50
1
Problems
50
7
Chapter 2 Boundary-Value Problems in Electrostatics: I
57
38
2.1 Method of Images
57
1
2.2 Point Charge in the Presence of a Grounded Conducting Sphere
58
2
2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere
60
1
2.4 Point Charge Near a Conducting Sphere at Fixed Potential
61
1
2.5 Conducting Sphere in a Uniform Electric Field by Method of Images
62
2
2.6 Green Function for the Sphere; General Solution for the Potential
64
1
2.7 Conducting Sphere with Hemispheres at Different Potentials
65
2
2.8 Orthogonal Functions and Expansions
67
3
2.9 Separation of Variables; Laplace Equation in Rectangular Coordinates
70
2
2.10 A Two-Dimensional Potential Problem; Summation of Fourier Series
72
3
2.11 Fields and Charge Densities in Two-Dimensional Corners and Along Edges
75
4
2.12 Introduction to Finite Element Analysis For Electrostatics
79
5
References and Suggested Reading
84
1
Problems
85
10
Chapter 3 Boundary-Value Problems in Electrostatics: II
95
50
3.1 Laplace Equation in Spherical Coordinates
95
1
3.2 Legendre Equation and Legendre Polynomials
96
5
3.3 Boundary-Value Problems with Azimuthal Symmetry
101
3
3.4 Behavior of Fields in a Conical Hole or Near a Sharp Point
104
3
3.5 Associated Legendre Functions and the Spherical Harmonics Y(lm) (Theta. Phi)
107
3
3.6 Addition Theorem for Spherical Harmonics
110
1
3.7 Laplace Equation in Cylindrical Coordinates: Bessel Functions
111
6
3.8 Boundary-Value Problems in Cylindrical Coordinates
117
2
3.9 Expansion of Green Functions in Spherical Coordinates
119
3.10 Solution of Potential Problems with the Spherical Green Function Expansion
112
3.11 Expansion of Green Functions in Cylindrical Coordinates
125
2
3.12 Eigenfunction Expansions for Green Functions
127
2
3.13 Mixed Boundary Conditions. Conducting Plane with a Circular Hole
129
6
References and Suggested Reading
135
1
Problems
135
10
Chapter 4 Multipoles, Electrostatics of Macroscopic Media, Dielectrics
145
29
4.1 Multipole Expansion
145
5
4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field
150
1
4.3 Elementary Treatment of Electrostatics with Ponderable Media
151
3
4.4 Boundary-Value Problems with Dielectrics
154
5
4.5 Molecular Polarizability and Electric Susceptibility
159
3
4.6 Models for Electric Polarizability
162
3
4.7 Electrostatic Energy in Dielectric Media
165
4
References and Suggested Reading
169
1
Problems
169
5
Chapter 5 Magnetostatics, Faraday's Law, Quasi-Static Fields
174
63
5.1 Introduction and Definitions
174
1
5.2 Biot and Savart Law
175
3
5.3 Differential Equations of Magnetostatics and Ampere's Law
178
2
5.4 Vector Potential
180
1
5.5 Vector Potential and Magnetic Induction for a Circular Current Loop
181
3
5.6 Magnetic Fields of a Localized Current Distribution, Magnetic Moment
184
4
5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction
188
3
5.8 Macroscopic Equations, Boundary Conditions on B and H
191
3
5.9 Methods of Solving Boundary-Value Problems in Magnetostatics
194
4
5.10 Uniformly Magetized Sphere
198
1
5.11 Magnetized Sphere in an External Field: Permanent Magnets
199
2
5.12 Magnetic Shielding, Spherical Shell of Permeable Material in a Uniform Field
201
2
5.13 Effect of a Circular Hole in a Perfectly Conducting Plane with an Asymptotically Uniform Tangential Magnetic Fields on One Side
203
3
5.14 Numerical Methods for Two-Dimensional Magnetic Fields
206
2
5.15 Faraday's Law of Induction
208
4
5.16 Energy in the Magnetic Field
212
3
5.17 Energy and Self-and Mutual Inductances
215
3
5.18 Quasi-Static Magnetic Fields in Conductors; Eddy Currents: Magnetic Diffusion
218
5
References and Suggested Reading
223
2
Problems
225
12
Chapter 6 Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws
237
58
6.1 Maxwell's Displacement Current; Maxwell Equations
237
2
6.2 Vector and Scalar Potentials
239
1
6.3 Gauge Transformations, Lorentz Gauge, Coulomb Gauge
240
3
6.4 Green Functions for the Wave Equation
243
3
6.5 Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulomb and Biot-Savart Laws; Heaviside-Feynman Expressions for Fields of Point Charge
246
2
6.6 Derivation for the Equations of Macroscopic Electromagnetism
248
10
6.7 Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields
258
4
6.8 Poynting's Theorem in Linear Dissipative Media with Losses
262
2
6.9 Poynting's Theorem for Harmonic Fields; Fields Definitions of Impedance and Admittance
264
3
6.10 Transformation Properties for Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal
267
6
6.11 On the Question of Magnetic Monopoles
273
2
6.12 Discussion of the Dirac Quantization Condition
275
5
6.13 Polarization Potentials (Hertz Vectors)
280
2
References and Suggested Reading
282
1
Problems
283
12
Chapter 7 Plane Electromagnetic Waves and Wave Propagation
295
57
7.1 Plane Waves in a Nonconducting Medium
295
4
7.2 Linear and Circular Polarization; Stockes Parameters
299
3
7.3 Reflection and Refraction of Electromagnetic Waves at a Plane Interface Between Two Dielectrics
302
4
7.4 Polarization by Reflection, Total Internal Reflection: Goos-Hanchen Effect
306
3
7.5 Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas
309
7
7.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere
316
3
7.7 Magnetohydrodynamic Waves
319
3
7.8 Superposition of the Waves in One Dimension; Group Velocity
322
4
7.9 Illustration of the Spreading of a Pulse As It Propagates in a Dispersive Medium
326
4
7.10 Causality in the Connection Between D and E: Kramers-Kroning Relations
330
5
7.11 Arrival of a Signal After Propagation Through a Dispersive Medium
335
4
References and Suggested Reading
339
1
Problems
340
12
Chapter 8 Waveguides, Resonant Cavities, and Optical Fibers
352
55
8.1 Fields at the Surface of and Within a Conductor
352
4
8.2 Cylindrical Cavities and Waveguides
356
3
8.3 Waveguides
359
2
8.4 Modes in a Rectangular Waveguides
361
2
8.5 Energy Flow and Attenuation in Waveguides
363
3
8.6 Perturbation of Boundary Conditions
366
2
8.7 Resonant Cavities
368
3
8.8 Power Losses in a Cavity; Q of a Cavity
371
3
8.9 Earth and Ionosphere as a Resonant Cavity: Schumann Resonances
374
4
8.10 Multimode Propagation in Optical Fibers
378
7
8.11 Modes in Dielectric Waveguides
385
4
8.12 Expansion in Normal Modes; Fields Generated by a Localized Source in a Hollow Metallic Guide
389
6
References and Suggested Reading
395
1
Problems
396
11
Chapter 9 Radiating Systems, Multipole Fields and Radiation
407
49
9.1 Fields and Radiation of a Localized Oscillating Source
407
3
9.2 Electric Dipole Fields and Radiation
410
3
9.3 Magnetic Dipole and Electric Quadrupole Fields
413
3
9.4 Center-Fed Linear Antenna
416
3
9.5 Multipole Expansion for Localized Source or Aperture in Waveguide
419
6
9.6 Spherical Wave Solutions of the Scalar Wave Equation
425
4
9.7 Multipole Expansion of the Electromagnetic Fields
429
3
9.8 Properties of Multipole Fields, Energy and Angular Momentum of Multipole Radiation
432
5
9.9 Angular Distribution of Multipole Radiation
437
2
9.10 Sources of Multipole Radiation; Multipole Moments
439
3
9.11 Multipole Radiation in Atoms and Nuclei
442
2
9.12 Multipole Radiation from a Linear, Center-Fed Antenna
444
4
References and Suggested Reading
448
1
Problems
449
7
Chapter 10 Scattering and Diffraction
456
58
10.1 Scattering at Long Wavelengths
456
6
10.2 Perturbation Theory of Scattering, Rayleigh's Explanation of the Blue Sky, Scattering by Gases and Liquids, Attenuation in Optical Fibers
462
9
10.3 Spherical Wave Expansion of a Vector Plane Wave
471
2
10.4 Scattering of Electromagnetic Waves by a Sphere
473
5
10.5 Scalar Diffraction Theory
478
4
10.6 Vector Equivalents of the Kirchhoff Integral
482
3
10.7 Vectorial Diffraction Theory
485
3
10.8 Babinet's Principle of Complementary Screens
488
2
10.9 Diffraction by a Circular Aperture; Remarks on Small Apertures
490
5
10.10 Scattering in the Short-Wavelength Limit
495
5
10.11 Optical Theorem and Related Matters
500
6
References and Suggested Reading
506
1
Problems
507
7
Chapter 11 / Special Theory of Relativity
514
65
11.1 The Situation Before 1900, Einstein's Two Postulates
515
3
11.2 Some Recent Experiments
518
6
11.3 Lorentz Transformations and Basic Kinematic Results of Special Relativity
524
6
11.4 Addition of Velocities; 4-Velocity
530
3
11.5 Relativistic Momentum and Energy of a Particle
533
6
11.6 Mathematical Properties of the Space-Time of Special Relativity
539
4
11.7 Matrix Representation of Lorentz Transformations, Infinitesimal Generators
543
5
11.8 Thomas Precession
548
5
11.9 Invariance of Electric Charge; Covariance of Electrodynamics
553
5
11.10 Transformation of Electromagnetic Fields
558
3
11.11 Relativistic Equation of Motion for Spin in Uniform or Slowly Varying External Fields
561
4
11.12 Note on Notation and Units in Relativistic Kinematics
565
1
References and Suggested Reading
566
2
Problems
568
11
Chapter 12 Dynamics of Relativistic Particles and Electromagnetic Fields
579
45
12.1 Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields
579
6
12.2 Motion in a Uniform, Static Magnetic Field
585
1
12.3 Motion in Combined, Uniform, Static Electric and Magnetic Fields
586
2
12.4 Particle Drifts in Nonuniform, Static Magnetic Fields
588
4
12.5 Adiabatic Invariance of Flux Through Orbit of Particle
592
4
12.6 Lowest Order Relativistic Corrections to the Lagrangian for Interacting Charged Particles: The Darwin Lagrangian
596
2
12.7 Lagrangian for the Electromagnetic Field
598
2
12.8 Proca Lagrangian; Photon Mass Effects
600
3
12.9 Effective "Photon" Mass in Superconductivity; London Penetration Depth
603
2
12.10 Canonical and Symmetric Stress Tensors; Conservation Laws
605
7
12.11 Solution of the Wave Equation in Covariant Form; Invariant Green Functions
612
3
References and Suggested Reading
615
2
Problems
617
7
Chapter 13 Collisions, Energy Loss, and Scattering of Charged Particles, Cherenkov and Transition Radiation
624
37
13.1 Energy Transfer in Coulomb Collision Between Heavy Incident Particle and Free Electron; Energy Loss in Hard Collisions
625
2
13.2 Energy Loss form Soft Collisions; Total Energy Loss
627
4
13.3 Density Effect in Collisional Energy Loss
631
6
13.4 Cherenkov Radiation
637
3
13.5 Elastic Scattering of Fast Charged Particles by Atoms
640
3
13.6 Mean Square Angle of Scattering; Angular Distribution of Multiple Scattering
643
3
13.7 Transition Radiation
646
8
References and Suggested Reading
654
1
Problems
655
6
Chapter 14 Radiation by Moving Charges
661
47
14.1 Lienard-Wiechert Potentials and Fields for a Point Charge
661
4
14.2 Total Power Radiated by an Accelerated Charge: Larmor's Formula and Its Relativistic Generalization
665
3
14.3 Angular Distribution of Radiation Emitted by an Accelerated Charge
668
3
14.4 Radiation Emitted by a Charge in Arbitrary, Extremely Relativistic Motion
671
2
14.5 Distribution in Frequency and Angle of Energy Radiated by Accelerated Charges: Basic Results
673
3
14.6 Frequency Spectrum of Radiation Emitted by a Relativistic Charged Particle in Instantaneously Circular Motion
676
7
14.7 Undulators and Wigglers for Synchrotron Light Sources
683
11
14.8 Thomson Scattering of Radiation
694
3
References and Suggested Reading
697
1
Problems
698
10
Chapter 15 Bremsstrahlung, Method of Virtual Quanta, Radiative Beta Processes
708
37
15.1 Radiation Emitted During Collissions
709
5
15.2 Bremsstrahlung in Coulomb Collisions
714
7
15.3 Screening Effects; Relativistic Radiative Energy Loss
721
3
15.4 Weizsacker-Williams Method of Virtual Quanta
724
5
15.5 Bremsstrahlung as the Scattering of Virtual Quanta
729
1
15.6 Radiation Emitted During Beta Decay
730
2
15.7 Radiation Emitted During Orbital Electron Capture: Disappearance of Charge and Magnetic Moment
732
5
References and Suggested Reading
737
1
Problems
737
8
Chapter 16 Radiation Damping, Classical Models of Charged Particles
745
30
16.1 Introductory Considerations
745
2
16.2 Radiative Reaction Force from Conservation of Energy
747
3
16.3 Abraham-Lorentz Evaluation of the Self-Force
750
5
16.4 Relativistic Coveriance; Stability and Poincare Stresses
755
2
16.5 Covariant Definitions of Electromagnetic Energy and Momentum
757
2
16.6 Covariant Stable Charged Particle
759
4
16.7 Level Breadth and Level Shift of a Radiating Oscillator
763
3
16.8 Scattering and Absorption of Radiation by an Oscillator
766
2
References and Suggested Reading
768
1
Problems
769
6
Appendix on Units and Dimensions
775
10
1 Units and Dimensions, Basic Units and Derived Units and Derived Units
775
2
2 Electromagnetic Units and Equations
777
2
3 Various Systems of Electromagnetic Units
779
3
4 Conversion of Equations and Amounts Between SI Units and Gaussian Units
782
3
Bibliography
785
6
Index
791