The Theory of the Electromagnetic Field

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ISBN: 9780139132933 | 0139132937
Cover: Hardcover
Copyright: 6/1/1975

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Preface	p. xiii
Introduction	p. 1
Mathematical and Physical Preliminaries	p. 5
Scalars, Vectors, and Vector Algebra	p. 5
The Representation of Fields	p. 13
Static Force Fields	p. 17
Coordinate-Free Definitions for the Gradient and the Curl	p. 24
Charge and Current: From Qualitative Recognition to Quantitative Measurement	p. 33
The Phenomenon of Electric Charge	p. 34
The Interaction of Point Charges	p. 35
The Phenomenon of Current	p. 38
The Interaction of Parallel Currents	p. 40
Current as Charge in Motion	p. 41
Units in Electricity and Magnetism	p. 42
Charge and Current: The Specification of Arbitrary Distributions	p. 50
Charge Density	p. 52
Current Density	p. 54
Mathematical Digression I: Stokes' Theorem and The Divergence Theorem	p. 61
The Equation of Continuity	p. 69
Mathematical Digression II: Several Operators Involving [down triangle, open]	p. 71
The Electromagnetic Field: Its Definition and Its Effect on General Charge Distributions	p. 74
Forces on Point Charges: A Definition of the Electromagnetic Field	p. 75
Trajectories of Particles in Prescribed Fields	p. 78
Forces and Torques on General Distributions in Prescribed Fields	p. 83
The Electric Field Produced by Static Charges	p. 91
Coulomb's Law and the Electrostatic Field of Given Sources	p. 91
Gauss's Law	p. 102
The Restricted Faraday Law	p. 109
The Electrostatic Potential	p. 110
Energy in the Electrostatic Field	p. 117
The Multipole Expansion of the Electrostatic Potential	p. 120
The Magnetic Induction Field Produced by Steady Currents	p. 129
The Law of Biot-Savart	p. 130
The Magnetic Flux Law	p. 138
Ampere's Circuital Law	p. 140
The Magnetic Vector Potential	p. 145
Energy in the Static Magnetic Induction Field	p. 150
The Multipole Expansion of the Magnetic Vector Potential	p. 151
The Electromagnetic Field Produced by Time-Dependent Charge Distributions: Maxwell's Equations in Vacuum	p. 156
Electromagnetic Induction: Faraday's Law	p. 157
A Contradiction and its Resolution: Displacement Current	p. 170
Maxwell's Equations	p. 172
Energy in the Electromagnetic Field	p. 176
Momentum in the Electromagnetic Field	p. 178
A Reformulation: Maxwell's Equations for the Potentials	p. 179
Another Reformulation: Decoupling the Equations for the Fields	p. 182
Interlude: A Change of View	p. 185
Plane Electromagnetic Waves in Vacuum	p. 187
Elementary Fields Depending on z and t; Plane Electromagnetic Waves	p. 188
Energy and Momentum in Plane Waves	p. 193
Superposition of Waves of the Same Frequency: Polarization and Interference	p. 195
Superposition of Waves of Different Frequencies; Spectral Decomposition	p. 204
Plane Waves in Three Dimensions	p. 207
Potential Theory	p. 213
Boundary Conditions	p. 214
Superposition and Uniqueness	p. 215
One-Dimensional Problems	p. 218
Two-Dimensional Problems by Separation of Variables	p. 218
Two-Dimensional Problems Using Complex Variables	p. 228
The Method of Images	p. 232
Numerical Solution of Laplace's Equation	p. 236
Solution of Laplace's Equation by Experiment: The Method of Analogy	p. 244
Poisson's Equation	p. 245
Properties of Matter I: Conduction	p. 249
Macroscopic Description: Conductivity and Ohm's Law	p. 250
Microscopic Description: Carrier Mobility and Collision Times	p. 254
Properties of Matter II: Dielectric Polarization	p. 260
The Microscopic Description: Electric Polarizability	p. 263
The Macroscopic Description: Dielectric Polarization	p. 267
The Macroscopic Scalar Potential and Electric Field at a Point Exterior to a Polarized Dielectric	p. 268
The Macroscopic Electric Field at a Point Interior to a Polarized Dielectric	p. 272
The Basic Equations of Electrostatics when Dielectrics are Present	p. 278
Connecting the Microscopic Polarizability with the Macroscopic Dielectric Constant: The Clausius-Mossotti Relation	p. 285
Properties of Matter III: Magnetization	p. 289
The Microscopic Description: Magnetic Polarizability	p. 290
The Macroscopic Description: Magnetization	p. 296
The Macroscopic Vector Potential and Magnetic Induction Field at a Point Exterior to a Magnetized Object: Bound Currents	p. 297
An Alternative Approach to the Exterior Field: Equivalent Poles	p. 305
The Macroscopic Magnetic Induction Field at a Point Interior to a Magnetized Object	p. 307
The Basic Equations of Magnetostatics when Magnetically Responsive Matter is Present	p. 310
Connecting the Microscopic Polarizability with the Macroscopic Relative Permeability	p. 315
Ferromagnetism	p. 317
Time-Dependent Fields When Matter Is Present: Maxwell's Equations Revised	p. 325
Maxwell's Equations in Matter	p. 326
The Equation of Continuity	p. 329
The Energy Theorem	p. 330
The Momentum Theorem	p. 332
On Which Fields are Basic	p. 333
The Potentials	p. 333
Boundary Conditions at Discontinuities in the Medium	p. 335
Static Potentials	p. 342
Plane Electromagnetic Waves in Linear Matter	p. 347
Maxwell's Equations for Monochromatic Fields in Linear Matter	p. 348
Boundary Conditions on Monochromatic Fields	p. 353
Plane Monochromatic Waves in Unbounded, Isotropic, Homogeneous, Linear Media	p. 356
Transmission and Reflection at Plane Interfaces	p. 363
Wave Guides and Cavity Resonators	p. 378
Superposition of Waves of Different Frequency: Dispersion	p. 387
Radiation from Prescribed Sources in Vacuum	p. 399
The General Solution of the Inhomogeneous Wave Equation; Retardation	p. 400
Radiation from Monochromatic Sources: The Oscillating Electric Dipole	p. 403
The Lienard-Wiechert Potentials	p. 408
The Fields of a Moving Point Charge	p. 412
Radiation from Accelerated Point Charges	p. 416
The Radiation Reaction	p. 422
Relativistic Formulation of Maxwell's Equations	p. 426
A Review of Special Relativity	p. 430
Maxwell's Equations in Covariant Form; The Electromagnetic Field Tensor	p. 438
Transformation of the Electromagnetic Field	p. 443
The Stress-Energy-Momentum Tensor	p. 445
A New Viewpoint: The Law of Biot-Savart Revisited	p. 448
Appendices
Linear Equations, Determinants, and Matrices	p. 459
Simultaneous Linear Equations and Determinants	p. 459
Matrix Algebra	p. 462
Binomial and Taylor Expansions	p. 467
Vector Identities and Relationships	p. 470
Complex Numbers and Fourier Analysis	p. 472
The Algebra of Complex Numbers	p. 472
Fourier Series	p. 477
Fourier Transforms	p. 479
Reference Tables	p. 481
Answers to Selected Problems	p. 483
Index	p. 499
Table of Contents provided by Ingram. All Rights Reserved.

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