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Tables of Contents for Introduction to Electrodynamics
Chapter/Section Title
Page #
Page Count
Preface
ix
Advertisement
xi
Vector Analysis
1
57
Vector Algebra
1
12
Vector Operations
1
3
Vector Algebra: Component Form
4
3
Triple Products
7
1
Position, Displacement, and Separation Vectors
8
2
How Vectors Transform
10
3
Differential Calculus
13
11
``Ordinary'' Derivatives
13
1
Gradient
13
3
The Operator &nable;
16
1
The Divergence
17
2
The Curl
19
1
Product Rules
20
2
Second Derivatives
22
2
Integral Calculus
24
14
Line, Surface, and Volume Integrals
24
1
The Fundamental Theorem of Calculus
24
5
The Fundamental Theorem for Gradients
29
2
The Fundamental Theorem for Divergences
31
3
The Fundamental Theorem for Curls
34
3
Integration by Parts
37
1
Curvilinear Coordinates
38
7
Spherical Polar Coordinates
38
5
Cylindrical Coordinates
43
2
The Dirac Delta Function
45
7
The Divergence of r/r2
45
1
The One-Dimensional Dirac Delta Function
46
4
The Three-Dimensional Delta Function
50
2
The Theory of Vector Fields
52
6
The Helmholtz Theorem
52
1
Potentials
53
5
Electrostatics
58
52
The Electric Field
58
7
Introduction
58
1
Coulomb's Law
59
1
The Electric Field
60
1
Continous Charge Distributions
61
4
Divergence and Curl of Electrostatic Fields
65
12
Field Lines, Flux, and Gauss's Law
65
4
The Divergence of E
69
1
Applications of Gauss's Law
70
6
The Curl of E
76
1
Electric Potential
77
13
Introduction of Potential
77
2
Comments on Potential
79
4
Poisson's Equation and Laplace's Equation
83
1
The Potential of a Localized Charge Distribution
83
4
Summary; Electrostatic Boundary Conditions
87
3
Work and Energy in Electrostatics
90
6
The Work Done to Move a Charge
90
1
The Energy of a Point Charge Distribution
91
2
The Energy of a Continuous Charge Distribution
93
2
Comments on Electrostatic Energy
95
1
Conductors
96
14
Basic Properties
96
2
Induced Charges
98
4
Surface Charge and the Force on a Conductor
102
1
Capacitors
103
7
Special Techniques
110
50
Laplace's Equation
110
11
Introduction
110
1
Laplace's Equation in One Dimension
111
1
Laplace's Equation in Two Dimensions
112
2
Laplace's Euqation in Three Dimensions
114
2
Boundary Conditions and Uniqueness Theorems
116
2
Conductors and the Second Uniqueness Theorem
118
3
The Method of Images
121
6
The Classic Image Problem
121
2
Induced Surface Charge
123
1
Force and Energy
123
1
Other Image Problems
124
3
Separation of Variables
127
19
Cartesian Coordinates
127
10
Spherical Coordinates
137
9
Multipole Expansion
146
14
Approximate Potentials at Large Distances
146
3
The Monopole and Dipole Terms
149
2
Origin of Coordinates in Multipole Expansions
151
2
The Electric Field of a Dipole
153
7
Electric Fields in Matter
160
42
Polarization
160
6
Dielectrics
160
1
Induced Dipoles
160
3
Alignment of Polar Molecules
163
3
Polarization
166
1
The Field of a Polarized Object
166
9
Bound Charges
166
4
Physical Interpretation of Bound Charges
170
3
The Field Inside a Dielectric
173
2
The Electric Displacement
175
4
Gauss's Law in the Presence of Dielectrics
175
3
A Deceptive Parallel
178
1
Boundary Conditions
178
1
Linear Dielectrics
179
23
Susceptibility, Permittivity, Dielectric Constant
179
7
Boundary Value Problems with Linear Dielectrics
186
5
Energy in Dielectric Systems
191
2
Forces on Dielectrics
193
9
Magnetostatics
202
53
The Lorentz Force Law
202
13
Magnetic Fields
202
2
Magnetic Forces
204
4
Currents
208
7
The Biot-Savart Law
215
6
Steady Currents
215
1
The Magnetic Field of a Steady Current
215
6
The Divergence and Curl of B
221
13
Straight-Line Currents
221
1
The Divergence and Curl of B
222
3
Applications of Ampere's Law
225
7
Comparison of Magnetostatics and Electrostatics
232
2
Magnetic Vector Potential
234
21
The Vector Potential
234
6
Summary; Magnetostatic Boundary Conditions
240
2
Multipole Expansion of the Vector Potential
242
13
Magnetic Fields in Matter
255
30
Magnetization
255
8
Diamagnets, Paramagnets, Ferromagnets
255
1
Torques and Forces on Magnetic Dipoles
255
5
Effect of a Magnetic Field on Atomic Orbits
260
2
Magnetization
262
1
The Field of a Magnetized Object
263
6
Bound Currents
263
3
Physical Interpretation of Bound Currents
266
2
The Magnetic Field Inside Matter
268
1
The Auxiliary Field H
269
5
Ampere's law in Magnetized Materials
269
4
A Deceptive Parallel
273
1
Boundary Conditions
273
1
Linear and Nonlinear Media
274
11
Magnetic Susceptibility and Permeability
274
4
Ferromagnetism
278
7
Electrodynamics
285
60
Electromotive Force
285
16
Ohm's Law
285
7
Electromotive Force
292
2
Motional emf
294
7
Electromagnetic Induction
301
20
Faraday's Law
301
4
The Induced Electric Field
305
5
Inductance
310
7
Energy in Magnetic Fields
317
4
Maxwell's Equations
321
24
Electrodynamics Before Maxwell
321
2
How Maxwell Fixed Ampere's Law
323
3
Maxwell's Equations
326
1
Magnetic Charge
327
1
Maxwell's Equations in Matter
328
3
Boundary Conditions
331
14
Conservation Laws
345
19
Charge and Energy
345
4
The Continuity Equation
345
1
Poynting's Theorem
346
3
Momentum
349
15
Newton's Thrid Law in Electrodynamics
349
2
Maxwell's Stress Tensor
351
4
Conservation of Momentum
355
3
Angular Momentum
358
6
Electromagnetic Waves
364
52
Waves in One Dimension
364
11
The Wave Equation
364
3
Sinusoidal Waves
367
3
Boundary Conditions: Reflection and Transmission
370
3
Polarization
373
2
Electromagnetic Waves in Vacuum
375
7
The Wave Eqation for E and B
375
1
Monochromatic Plane Waves
376
4
Energy and Momentum in Electromagnetic Waves
380
2
Electromagnetic Waves in Matter
382
10
Propagation in Linear Media
382
2
Reflection and Transmission at Normal Incidence
384
2
Reflection and Transmission at Oblique Incidence
386
6
Absorption and Dispersion
392
13
Electromagnetic Waves in Conductors
392
4
Reflection at a Conducting Surface
396
2
The Frequency Dependence of Permittivity
398
7
Guided Waves
405
11
Wave Guides
405
3
TE Waves in a Rectangular Wave Guide
408
3
The Coaxial Transmission Line
411
5
Potentials and Fields
416
27
The Potential Formulation
416
6
Scalar and Vector Potentials
416
3
Gauge Transformations
419
2
Coulomb Gauge and Lorentz Gauge
421
1
Continuous Distributions
422
7
Retarded Potentials
427
1
Jefimenko's Equations
427
2
Point Charges
429
14
Lienard-Wiechert Potentials
429
6
The Fields of a Moving Point Charge
435
8
Radiation
443
34
Dipole Radiation
443
17
What is Radiation?
443
1
Electric Dipole Radiation
444
7
Magnetic Dipole Radiation
451
3
Radiation from an Arbitrary Source
454
6
Point Charges
460
17
Power Radiated by a Point Charge
460
5
Radiation Reaction
465
4
The Physical Basis of the Radiation Reaction
469
8
Electrodynamics and Relativity
477
70
The Special Theory of Relativity
477
30
Einstein's Postulates
477
6
The Geometry of Relativity
483
10
The Lorentz Transformations
493
7
The Structure of Spacetime
500
7
Relativistic Mechanics
507
15
Proper Time and Proper Velocity
507
2
Relativistic Energy and Momentum
509
2
Relativistic Kinematics
511
5
Relativistic Dynamics
516
6
Relativistic Electrodynamics
522
25
Magnetism as a Relativistic Phenomenon
522
3
How the Fields Transform
525
10
The Field Tensor
535
2
Electrodynamics in Tensor Notation
537
4
Relativistic Potentials
541
6
A Vector Calculus in Curvilinear Coordinates
547
8
A.1 Introduction
547
1
A.2 Notation
547
1
A.3 Gradient
548
1
A.4 Divergence
549
3
A.5 Curl
552
2
A.6 Laplacian
554
1
B The Helmholtz Theorem
555
3
C Units
558
4
Index
562