Electrodynamics: An Introduction Including Quantum Effects

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ISBN: 9789812388087 | 9812388087
Cover: Paperback
Copyright: 9/30/2004

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An extensive text on electrodynamics with detailed explanations and calculations. One hundred worked examples have been incorporated, making the book suitable also for self-instruction. Apart from all traditional topics of Maxwell theory, the book includes the special theory of relativity and the Lagrangian formalism and applications; the text also contains introductions to quantum effects related to electrodynamics, such as the Aharonov-Bohm and the Casimir effects. Numerous modern applications in diverse directions are treated in the examples.

Preface

xiii

Introduction

(8)

What is Electrodynamics?

(1)

Presentation of Macroscopic Electrodynamics

(5)

On the Choice of Units

(3)

Electrostatics -- Basic Aspects

(38)

Introductory Remarks

(1)

The Coulomb Law

(3)

The Electrostatic Potential

(2)

The Equations of Electrostatics

(3)

Dirac's Delta Distribution

(6)

Potential Energy of Charges in Electric Fields

(1)

The Electric Field at Charged Surfaces

(3)

Examples

(6)

Conductors and Electrical Screening

(8)

Energy of Charge Distributions

(6)

Applications of Electrostatics

(38)

Introductory Remarks

(1)

Method I: The Gauss Law

(1)

Method II: Poisson and Laplace Equations

(2)

Method III: Direct Integration

(1)

Method IV: Kelvin's Method of Image Charges

(3)

Theoretical Aspects of Image Charges

(13)

The Induced Charge

(4)

Green's Theorems

(3)

Green's Function and Image Potential

(2)

The Image Potential in an Example

(4)

Method V: Conjugate Functions

(6)

Orthogonal Functions

(6)

Orthogonal Functions in General

(2)

Fourier Series, Fourier Expansions

(2)

Spherical Functions (Legendre, Associated Legendre, Hyperspherical Functions)

(2)

The Multipole Expansion

(7)

Macroscopic Electrostatics

(24)

Introductory Remarks

(1)

Dielectrics and Dielectric Displacement

(8)

The Behaviour of D at an Interface

(1)

Examples

(3)

Polarisation of a Sphere in an Electric Field E0

(5)

Energy of the Electric Field

102

(4)

The Energy Density Formula

102

(2)

Polarisation Energy

104

(2)

Summary of Formulae of Electrostatics

106

(3)

Magnetostatics

109

(26)

Introductory Remarks

109

(1)

Continuity Equation and Stationary Current

109

(4)

Ampere's Experiments and the Law of Biot and Savart

113

(6)

Examples

119

(4)

The Electromagnetic Vector Potential A

123

(3)

Integral Form of Ampere's Law

126

(1)

Further Examples

127

(8)

Macroscopic Magnetostatics

135

(16)

Introductory Remarks

135

(1)

Macroscopic Magnetisation

136

(5)

Magnetic Properties of Matter

141

(1)

Energy of the Magnetic Field

142

(1)

Behaviour of B and H at Boundary Surfaces

142

(2)

Current Circuits Compared with Flux Circuits

144

(1)

Examples

145

(5)

Summary of Formulae of Magnetostatics

150

(1)

The Maxwell Equations

151

(22)

Preliminary Remarks

151

(1)

Time-Dependent Fields and Faraday's Law of Induction

151

(5)

Energy of the Magnetic Field

156

(1)

The Generalised Ohm's Law

157

(1)

E and B with Time-Dependent Potentials

158

(1)

Displacement Current and Maxwell Equations

158

(4)

Poynting Vector and Conservation of Energy

162

(5)

Application: The Conduction Wire

164

(1)

The Field Momentum Density

165

(2)

Further Examples

167

(6)

Applications to Coils and Circuits

173

(22)

Introductory Remarks

173

(1)

Inductances Lij

173

(2)

Examples

175

(3)

The Vector Potential of a Long Solenoid

178

(5)

Energy of a Self-Inductance

183

(6)

Simple Current Circuits

189

(3)

Current Circuits with R and L

189

(2)

Circuits with L, C and R

191

(1)

Self-Inductances: Conjugate Function Method

192

(3)

Electromagnetic Waves

195

(14)

Introductory Remarks

195

(1)

Electromagnetic Waves in Vacuum

195

(5)

Electromagnetic Waves in Media

200

(1)

Frequency Dependence of ε and σ

201

(6)

The Generalised Dielectric Constant

201

(1)

Frequency Dependence of σ

202

(5)

The (Normal) Skin Effect

207

(2)

Moving Charges in Vacuum

209

(34)

Introductory Remarks

209

(1)

Maxwell's Equations for Moving Charges

209

(6)

The Lienard--Wiechert Potentials of a Moving Point Charge

215

(3)

The Fields E, B of a Moving Point Charge

218

(10)

The Hertz Dipole

228

(5)

The Potentials

228

(3)

The Field Strengths

231

(2)

Current Element Ids and Dipole Radiation

233

(4)

The Power of an Oscillating Dipole

234

(2)

Radiation Resistance

236

(1)

Further Examples

237

(6)

The Laws of Optics

243

(24)

Introductory Remarks

243

(1)

Continuity Conditions and Definition of the Surface Current

243

(4)

Electromagnetic Waves in Media

247

(3)

Kinematical Aspects of Reflection and Refraction: Snell's Law

250

(3)

Preliminary Remarks

250

(2)

Kinematical Aspects of Reflection and Refraction

252

(1)

Dynamical Aspects of Reflection and Refraction: The Fresnel Formulae

253

(11)

The Conditions

253

(1)

Two Cases of Linear Polarisation

254

(6)

The Brewster Angle and the Case without Reflection

260

(1)

The General Case

260

(1)

Total Reflection

261

(3)

Useful Formulation of the Fresnel Formulae

264

(3)

Metals

267

(10)

Introductory Remarks

267

(1)

Reflection and Absorption of Plane Waves by Metals

267

(3)

The Theory of Drude

270

(7)

Propagation of Radio Waves in the Ionosphere

277

(12)

Introductory Remarks

277

(1)

Condition for Return of Waves

278

(4)

Effect of Terrestrial Magnetic Field

282

(7)

Wave Guides and Resonators

289

(56)

What are Wave Guides?

289

(2)

Transverse Fields Derived from Longitudinal Fields

291

(3)

Boundary Conditions

294

(2)

Wave Guides and their TEM Fields

296

(4)

TEM Fields

296

(3)

The Coaxial Transmission Cable

299

(1)

Fundamental Equations for the Coaxial Cable

300

(4)

TM and TE Waves in Wave Guides

304

(12)

General Considerations

304

(1)

Wave Guides with Rectangular Cross Section

305

(9)

Wave Guides with Circular Cross Section

314

(2)

Alternative Treatment using Scalar and Vector Potentials

316

(3)

Wave Velocities

319

(1)

Energy Transport in Wave Guides

320

(12)

The Complex Poynting Vector

320

(2)

Application of the Complex Poynting Vector

322

(2)

Attenuation of Wave Guides (σ ≠ 0)

324

(5)

Optimal Use of a Wave Guide

329

(3)

Resonators (Closed Wave Guides)

332

(7)

Examples

339

(6)

Propagation of Waves in Media

345

(16)

Introductory Remarks

345

(1)

Dispersion Relation: Normal and Anomalous Dispersion

345

(3)

Absorption, Causality and Analyticity

348

(8)

Properties of A(w)

349

(3)

Properties of n(w)

352

(4)

No Wave Packet with a Velocity > c

356

(1)

Explanation of the Anomalous Dispersion

357

(4)

Causality and Dispersion Relations

361

(20)

Introductory Remarks

361

(1)

Cause U and Effect E

361

(1)

(U, E)-Linearity and Green's Functions

362

(2)

Causality

364

(2)

Causality and Analyticity

366

(2)

Principal Value Integrals and Dispersion Relations

368

(4)

Absorption: Special Cases

372

(2)

Comments on Principal Values

374

(4)

Subtracted Dispersion Relations

378

(3)

Covariant Formulation of Electrodynamics

381

(42)

Introductory Remarks

381

(1)

The Special Theory of Relativity

381

(7)

Introduction

381

(6)

Einstein's Interpretation of Lorentz Transformations

387

(1)

Minkowski Space

388

(4)

The 10-Parametric Poincare Group

392

(5)

Covariant and Contravariant Derivatives

396

(1)

Construction of the Field Tensor Fμν

397

(7)

Transformation from Rest Frame to Inertial Frame

404

(7)

Covariant Form of Maxwell's Equations

411

(2)

Covariantised Newton Equation of a Charged Particle

413

(4)

Examples

417

(6)

The Lagrange Formalism for the Electromagnetic Field

423

(24)

Introductory Remarks

423

(1)

Euler-Lagrange Equation

423

(2)

Symmetries and Energy-Momentum Tensor

425

(3)

The Lagrangian of the Electromagnetic Field

428

(4)

Gauge Invariance and Charge Conservation

432

(1)

Lorentz Transformations and Associated Conservation Laws

433

(1)

Masslessness of the Electromagnetic Field

434

(2)

Transversality of the Electromagnetic Field

436

(1)

The Spin of the Photon

437

(3)

Examples

440

(7)

The Gauge Covariant Schrodinger Equation and the Aharonov--Bohm Effect

447

(14)

Introductory Remarks

447

(1)

Schrodinger Equation of a Charged Particle in an Electromagnetic Field

448

(5)

Hamiltonian of a Charge in an Electromagnetic Field

448

(2)

The Gauge Covariant Schrodinger Equation

450

(3)

The Aharonov-Bohm Effect

453

(8)

Quantisation of the Electromagnetic Field and the Casimir Effect

461

(18)

Introductory Remarks

461

(1)

Quantisation of the n-Dimensional Harmonic Oscillator

462

(2)

Hamiltonian of the Gauge Field

464

(1)

Quantisation of the Electromagnetic Field

465

(5)

One-dimensional Illustration of the Casimir Effect

470

(4)

The Three-Dimensional Case

474

(5)

Duality and Magnetic Monopoles

479

(16)

Symmetrisation of the Maxwell Equations

479

(4)

Quantisation of Electric Charge

483

(3)

The Field of the Monopole

486

(1)

Uniqueness of the Wave Function

487

(3)

Regularisation of the Monopole Field

490

(3)

Concluding Remarks

493

(2)

A The Delta Distribution

495

(10)

B Units and Physical Constants

505

(8)

C Formulae

513

(2)

C.1 Vector Products

513

(1)

C.2 Integral Theorems

514

(1)

Bibliography

515

(2)

Index

517

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Electrodynamics: An Introduction Including Quantum Effects

Summary

Table of Contents

Supplemental Materials