Classical Electricity and Magnetism Second Edition

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

• ISBN13: 9780486439242
• ISBN10: 0486439240
• Edition: 2nd
• Format: Paperback
• Copyright: 2005-01-26
• Publisher: Dover Publications

Summary

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.

Table of Contents

ERRATA	xv
CHAPTER 1. THE ELECTROSTATIC FIELD IN VACUUM	1	(27)
1-1 Vector fields	1	(6)
1-2 The electric field	7	(1)
1-3 Coulomb's law	8	(2)
1-4 The electrostatic potential	10	(1)
1-5 The potential in terms of charge distribution	11	(2)
1-6 Field singularities	13	(1)
1-7 Clusters of point charges	13	(6)
1-8 Dipole interactions	19	(1)
1-9 Surface singularities	20	(3)
1-10 Volume distributions of dipole moment	23	(5)
CHAPTER 2. BOUNDARY CONDITIONS AND RELATION OF MICROSCOPIC TO MACROSCOPIC FIELDS	28	(14)
2-1 The displacement vector	28	(3)
2-2 Boundary conditions	31	(2)
2-3 The electric field in a material medium	33	(5)
2-4 Polarizability	38	(4)
CHAPTER 3. GENERAL METHODS FOR THE SOLUTION OF POTENTIAL PROBLEMS	42	(19)
3-1 Uniqueness theorem	42	(1)
3-2 Green's reciprocation theorem	43	(1)
3-3 Solution by Green's function	44	(3)
3-4 Solution by inversion	47	(2)
3-5 Solution by electrical images	49	(4)
3-6 Solution of Laplace's equation by the separation of variables	53	(8)
CHAPTER 4. TWO-DIMENSIONAL POTENTIAL PROBLEMS	61	(20)
4-1 Conjugate complex functions	61	(2)
4-2 Capacity and field strength	63	(1)
4-3 The potential of a uniform field	64	(1)
4-4 The potential of a line charge	64	(2)
4-5 Complex transformations	66	(1)
4-6 General Schwarz transformation	67	(3)
4-7 Single-angle transformations	70	(1)
4-8 Multiple-angle transformations	71	(2)
4-9 Direct solution of Laplace's equation by the method of harmonics	73	(1)
4-10 Illustration: Line charge and dielectric cylinder	74	(3)
4-11 Line charge in an angle between two conductors	77	(4)
CHAPTER 5. THREE-DIMENSIONAL POTENTIAL PROBLEMS	81	(14)
5-1 The solution of Laplace's equation in spherical coordinates	81	(1)
5-2 The potential of a point charge	82	(1)
5-3 The potential of a dielectric sphere and a point charge	83	(1)
5-4 The potential of a dielectric sphere in a uniform field	84	(2)
5-5 The potential of an arbitrary axially-symmetric spherical potential distribution	86	(1)
5-6 The potential of a charged ring	87	(1)
5-7 Problems not having axial symmetry	88	(1)
5-8 The solution of Laplace's equation in cylindrical coordinates	88	(3)
5-9 Application of cylindrical solutions to potential problems	91	(4)
CHAPTER 6. ENERGY RELATIONS AND FORCES IN THE ELECTRO-STATIC FIELD	95	(23)
6-1 Field energy in free space	95	(3)
6-2 Energy density within a dielectric	98	(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	42	(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