Classical Electrodynamics, 3rd Edition

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ISBN: 9780471309321 | 047130932X
Cover: Hardcover
Copyright: 8/14/1998

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A revision of the defining book covering the physics and classical mathematics necessary to understand electromagnetic fields in materials and at surfaces and interfaces. The third edition has been revised to address the changes in emphasis and applications that have occurred in the past twenty years.

Introduction and Survey

(23)

1.1 Maxwell Equations in Vacuum, Fields, and Sources

(3)

1.2 Inverse Square Law, or the Mass of the Photon

(4)

1.3 Linear Superposition

(4)

1.4 Maxwell Equations in Macroscopic Media

(3)

1.5 Boundary Conditions at Interfaces Between Different Media

(3)

1.6 Some Remarks on Idealizations in Electromagnetism

(3)

References and Suggested Reading

(2)

Chapter 1 Introduction to Electrostatics

(33)

1.1 Coulomb's Law

(1)

1.2 Electric Field

(3)

1.3 Gauss's Law

(1)

1.4 Differential Form of Gauss's Law

(1)

1.5 Another Equation of Electrostatics and the Scalar Potential

(2)

1.6 Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential

(3)

1.7 Poisson and Laplace Equations

(1)

1.8 Green's Theorem

(2)

1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions

(1)

1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function

(2)

1.11 Electrostatic Potential Energy and Energy Density; Capacitance

(3)

1.12 Variational Approach to the Solution of the Laplace and Poisson Equations

(4)

1.13 Relaxation Method for Two-Dimensional Electrostatic Problems

(3)

References and Suggested Reading

(1)

Problems

(7)

Chapter 2 Boundary-Value Problems in Electrostatics: I

(38)

2.1 Method of Images

(1)

2.2 Point Charge in the Presence of a Grounded Conducting Sphere

(2)

2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere

(1)

2.4 Point Charge Near a Conducting Sphere at Fixed Potential

(1)

2.5 Conducting Sphere in a Uniform Electric Field by Method of Images

(2)

2.6 Green Function for the Sphere; General Solution for the Potential

(1)

2.7 Conducting Sphere with Hemispheres at Different Potentials

(2)

2.8 Orthogonal Functions and Expansions

(3)

2.9 Separation of Variables; Laplace Equation in Rectangular Coordinates

(2)

2.10 A Two-Dimensional Potential Problem; Summation of Fourier Series

(3)

2.11 Fields and Charge Densities in Two-Dimensional Corners and Along Edges

(4)

2.12 Introduction to Finite Element Analysis For Electrostatics

(5)

References and Suggested Reading

(1)

Problems

(10)

Chapter 3 Boundary-Value Problems in Electrostatics: II

(50)

3.1 Laplace Equation in Spherical Coordinates

(1)

3.2 Legendre Equation and Legendre Polynomials

(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

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