Classical Electricity and Magnetism Second Edition

, by Panofsky, Wolfgang K. H.; Phillips, Melba

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ISBN: 9780486439242 | 0486439240
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Copyright: 1/26/2005

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Compact and precise, this text offers advanced undergraduates and graduate students a diverse selection of topics: the electrostatic field in vacuum; general methods for the solution of potential problems; radiation reaction and covariant formulation of the conservation laws of electrodynamics; and numerous other subjects. 119 figures. 10 tables. 1962 edition.

ERRATA

CHAPTER 1. THE ELECTROSTATIC FIELD IN VACUUM

(27)

1-1 Vector fields

(6)

1-2 The electric field

(1)

1-3 Coulomb's law

(2)

1-4 The electrostatic potential

(1)

1-5 The potential in terms of charge distribution

(2)

1-6 Field singularities

(1)

1-7 Clusters of point charges

(6)

1-8 Dipole interactions

(1)

1-9 Surface singularities

(3)

1-10 Volume distributions of dipole moment

(5)

CHAPTER 2. BOUNDARY CONDITIONS AND RELATION OF MICROSCOPIC TO MACROSCOPIC FIELDS

(14)

2-1 The displacement vector

(3)

2-2 Boundary conditions

(2)

2-3 The electric field in a material medium

(5)

2-4 Polarizability

(4)

CHAPTER 3. GENERAL METHODS FOR THE SOLUTION OF POTENTIAL PROBLEMS

(19)

3-1 Uniqueness theorem

(1)

3-2 Green's reciprocation theorem

(1)

3-3 Solution by Green's function

(3)

3-4 Solution by inversion

(2)

3-5 Solution by electrical images

(4)

3-6 Solution of Laplace's equation by the separation of variables

(8)

CHAPTER 4. TWO-DIMENSIONAL POTENTIAL PROBLEMS

(20)

4-1 Conjugate complex functions

(2)

4-2 Capacity and field strength

(1)

4-3 The potential of a uniform field

(1)

4-4 The potential of a line charge

(2)

4-5 Complex transformations

(1)

4-6 General Schwarz transformation

(3)

4-7 Single-angle transformations

(1)

4-8 Multiple-angle transformations

(2)

4-9 Direct solution of Laplace's equation by the method of harmonics

(1)

4-10 Illustration: Line charge and dielectric cylinder

(3)

4-11 Line charge in an angle between two conductors

(4)

CHAPTER 5. THREE-DIMENSIONAL POTENTIAL PROBLEMS

(14)

5-1 The solution of Laplace's equation in spherical coordinates

(1)

5-2 The potential of a point charge

(1)

5-3 The potential of a dielectric sphere and a point charge

(1)

5-4 The potential of a dielectric sphere in a uniform field

(2)

5-5 The potential of an arbitrary axially-symmetric spherical potential distribution

(1)

5-6 The potential of a charged ring

(1)

5-7 Problems not having axial symmetry

(1)

5-8 The solution of Laplace's equation in cylindrical coordinates

(3)

5-9 Application of cylindrical solutions to potential problems

(4)

CHAPTER 6. ENERGY RELATIONS AND FORCES IN THE ELECTRO-STATIC FIELD

(23)

6-1 Field energy in free space

(3)

6-2 Energy density within a dielectric

(2)

6-3 Thermodynamic interpretation of U

100

(1)

6-4 Thomson's theorem

101

(2)

6-5 Maxwell stress tensor

103

(4)

6-6 Volume forces in the electrostatic field in the presence of dielectrics

107

(4)

6-7 The behavior of dielectric liquids in an electrostatic field

111

(7)

CHAPTER 7. STEADY CURRENTS AND THEIR INTERACTION

118

(21)

7-1 Ohm's law

118

(1)

7-2 Electromotive force

119

(1)

7-3 The solution of stationary current problems

120

(2)

7-4 Time of relaxation in a homogeneous medium

122

(1)

7-5 The magnetic interaction of steady line currents

123

(2)

7-6 The magnetic induction field

125

(1)

7-7 The magnetic scalar potential

125

(2)

7-8 The magnetic vector potential

127

(2)

7-9 Types of currents

129

(1)

7-10 Polarization currents

129

(1)

7-11 Magnetic moments

130

(4)

7-12 Magnetization and magnetization currents

134

(1)

7-13 Vacuum displacement current

135

(4)

CHAPTER 8. MAGNETIC MATERIALS AND BOUNDARY VALUE PROBLEMS

139

(19)

8-1 Magnetic field intensity

139

(1)

8-2 Magnetic sources

140

(4)

8-3 Permeable media: magnetic susceptibility and boundary conditions

144

(1)

8-4 Magnetic circuits

145

(1)

8-5 Solution of boundary value problems by magnetic scalar potentials

146

(1)

8-6 Uniqueness theorem for the vector potential

147

(1)

8-7 The use of the vector potential in the solution of problems

148

(3)

8-8 The vector potential in two dimensions

151

(2)

8-9 The vector potential in cylindrical coordinates

153

(5)

CHAPTER 9. MAXWELL'S EQUATIONS

158

(12)

9-1 Faraday's law of induction

158

(1)

9-2 Maxwell's equations for stationary media

159

(1)

9-3 Faraday's law for moving media

160

(3)

9-4 Maxwell's equations for moving media

163

(2)

9-5 Motion of a conductor in a magnetic field

165

(5)

CHAPTER 10. ENERGY, FORCE, AND MOMENTUM RELATIONS IN THE ELECTROMAGNETIC FIELD

170

(15)

10-1 Energy relations in quasi-stationary current systems

170

(2)

10-2 Forces on current systems

172

(2)

10-3 Inductance

174

(3)

10-4 Magnetic volume force

177

(1)

10-5 General expressions for electromagnetic energy

178

(3)

10-6 Momentum balance

181

(4)

CHAPTER 11. THE WAVE EQUATION AND PLANE WAVES

185

(20)

11-1 The wave equation

185

(2)

11-2 Plane waves

187

(4)

11-3 Radiation pressure

191

(2)

11-4 Plane waves in a moving medium

193

(2)

11-5 Reflection and refraction at a plane boundary

195

(5)

11-6 Waves in conducting media and metallic reflection

200

(2)

11-7 Group velocity

202

(3)

CHAPTER 12. CONDUCTING FLUIDS IN A MAGNETIC FIELD (MAGNETOHYDRODYNAMICS)

205

(7)

12-1 "Frozen-in" lines of force

205

(2)

12-2 Magnetohydrodynamic waves

207

(5)

CHAPTER 13. WAVES IN THE PRESENCE OF METALLIC BOUNDARIES

212

(28)

13-1 The nature of metallic boundary conditions

212

(2)

13-2 Eigenfunctions and eigenvalues of the wave equation

214

(4)

13-3 Cavities with rectangular boundaries

218

(1)

13-4 Cylindrical cavities

219

(3)

13-5 Circular cylindrical cavities

222

(1)

13-6 Wave guides

223

(3)

13-7 Scattering by a circular cylinder

226

(3)

13-8 Spherical waves

229

(4)

13-9 Scattering by a sphere

233

(7)

CHAPTER 14. THE INHOMOGENEOUS WAVE EQUATION

240

(32)

14-1 The wave equation for the potentials

240

(2)

14-2 Solution by Fourier analysis

242

(3)

14-3 The radiation fields

245

(3)

14-4 Radiated energy

248

(6)

14-5 The Hertz potential

254

(1)

14-6 Computation of radiation fields by the Hertz method

255

(2)

14-7 Electric dipole radiation

257

(3)

14-8 Multipole radiation

260

(4)

14-9 Derivation of multipole radiation from scalar superpotentials

264

(3)

14-10 Energy and angular momentum radiated by multipoles

267

(5)

CHAPTER 15. THE EXPERIMENTAL BASIS FOR THE THEORY OF SPECIAL RELATIVITY

272

(14)

15-1 Galilean relativity and electrodynamics

272

(2)

15-2 The search for an absolute ether frame

274

(4)

15-3 The Lorentz-Fitzgerald contraction hypothesis

278

(1)

15-4 "Ether drag"

279

(1)

15-5 Emission theories

280

(3)

15-6 Summary

283

(3)

CHAPTER 16. RELATIVISTIC KINEMATICS AND THE LORENTZ TRANSFORMATION

286

(19)

16-1 The velocity of light and simultaneity

286

(2)

16-2 Kinematic relations in special relativity

288

(5)

16-3 The Lorentz transformation

293

(4)

16-4 Geometric interpretations of the Lorentz transformation

297

(4)

16-5 Transformation equations for velocity

301

(4)

CHAPTER 17. COVARIANCE AND RELATIVISTIC MECHANICS

305

(19)

17-1 The Lorentz transformation of a four-vector

305

(2)

17-2 Some tensor relations useful in special relativity

307

(4)

17-3 The conservation of momentum

311

(2)

17-4 Relation of energy to momentum and to mass

313

(3)

17-5 The Minkowski force

316

(2)

17-6 The collision of two similar particles

318

(2)

17-7 The use of four-vectors in calculating kinematic relations for collisions

320

(4)

CHAPTER 18. COVARIANT FORMULATION OF ELECTRODYNAMICS

324

(17)

18-1 The four-vector potential

324

(3)

18-2 The electromagnetic field tensor

327

(4)

18-3 The Lorentz force in vacuum

331

(1)

18-4 Covariant description of sources in material media

332

(2)

18-5 The field equations in a material medium

334

(2)

18-6 Transformation properties of the partial fields

336

(5)

CHAPTER 19. THE LIÉNARD-WIECHERT POTENTIALS AND THE FIELD OF A UNIFORMLY MOVING ELECTRON

341

(13)

19-1 The Liénard-Wiechert potentials

341

(3)

19-2 The fields of a charge in uniform motion

344

(3)

19-3 Direct solution of the wave equation

347

(1)

19-4 The "convection potential"

348

(2)

19-5 The virtual photon concept

350

(4)

CHAPTER 20. RADIATION FROM AN ACCELERATED CHARGE

354

(23)

20-1 Fields of an accelerated charge

354

(4)

20-2 Radiation at low velocity

358

(1)

20-3 The case of u parallel to u

359

(4)

20-4 Radiation when the acceleration is perpendicular to the velocity (radiation from circular orbits)

363

(7)

20-5 Radiation with no restrictions on the acceleration or velocity

370

(1)

20-6 Classical cross section for bremsstrahlung in a Coulomb field

371

(2)

20-7 Cerenkov radiation

373

(4)

CHAPTER 21. RADIATION REACTION AND COVARIANT FORMULATION OF THE CONSERVATION LAWS OF ELECTRODYNAMICS

377

(24)

21-1 Covariant formulation of the conservation laws of vacuum electrodynamics

377

(2)

21-2 Transformation properties of the "free" radiation field

379

(1)

21-3 The electromagnetic energy momentum tensor in material media

380

(1)

21-4 Electromagnetic mass

381

(2)

21-5 Electromagnetic mass-qualitative considerations

383

(3)

21-6 The reaction necessary to conserve radiated energy

386

(1)

21-7 Direct computation of the radiation reaction from the retarded fields

387

(2)

21-8 Properties of the equation of motion

389

(1)

21-9 Covariant description of the mechanical properties of the electromagnetic field of a charge

390

(2)

21-10 The relativistic equations of motion

392

(2)

21-11 The integration of the relativistic equation of motion

394

(1)

21-12 Modification of the theory of radiation to eliminate divergent mass integrals. Advanced potentials

394

(4)

21-13 Direct calculation of the relativistic radiation reaction

398

(3)

CHAPTER 22. RADIATION, SCATTERING, AND DISPERSION

401

(24)

22-1 Radiative damping of a charged harmonic oscillator

401

(2)

22-2 Forced vibrations

403

(1)

22-3 Scattering by an individual free electron

404

(3)

22-4 Scattering by a bound electron

407

(1)

22-5 Absorption of radiation by an oscillator

407

(2)

22-6 Equilibrium between an oscillator and a radiation field

409

(2)

22-7 Effect of a volume distribution of scatterers

411

(3)

22-8 Scattering from a volume distribution. Rayleigh scattering

414

(2)

22-9 The dispersion relation

416

(3)

22-10 A general theorem on scattering and absorption

419

(6)

CHAPTER 23. THE MOTION OF CHARGED PARTICLES IN ELECTRO-MAGNETIC FIELDS

425

(21)

23-1 World-line description

(385)

23-2 Hamiltonian formulation and the transition to three-dimensional formalism

427

(3)

23-3 Equations for the trajectories

430

(3)

23-4 Applications

433

(4)

23-5 The motion of a particle with magnetic moment in an electromagnetic field

437

(9)

CHAPTER 24. HAMILTONIAN FORMULATION OF MAXWELL'S EQUATIONS

446

(13)

24-1 Transition to a one-dimensional continuous system

446

(2)

24-2 Generalization to a three-dimensional continuum

448

(3)

24-3 The electromagnetic field

451

(3)

24-4 Periodic solutions in a box. Plane wave representation

454

(5)

APPENDIX I. UNITS AND DIMENSIONS IN ELECTROMAGNETIC THEORY

459

(11)

Tables: I-1. Conversion Factors

465

(5)

I-2. Fundamental Electromagnetic Relations Valid in vacuo as They Appear in the Various Systems of Units

466

(2)

I-3. Definition of Fields from Sources (mks system)

468

(1)

I-4. Useful Numerical Relations

469

(1)

APPENDIX II. USEFUL VECTOR RELATIONS

470

(3)

Table II-1. Vector Formulas

470

(3)

APPENDIX III. VECTOR RELATIONS IN CURVILINEAR COORDINATES

473

(6)

Table III-1. Coordinate Systems

475

(4)

BIBLIOGRAPHY

479

(6)

INDEX

485

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Classical Electricity and Magnetism Second Edition

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