Classical Electricity and Magnetism Second Edition,9780486439242

Classical Electricity and Magnetism Second Edition

by ;
Edition: 2nd
ISBN13: 9780486439242
ISBN10: 0486439240
Format: Paperback
Pub. Date: 2005-01-26
Publisher(s): Dover Publications
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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

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