Landau / Bell / Kearsley Electrodynamics of Continuous Media

2. Auflage 2013
ISBN: 978-1-4832-9375-2
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band Volume 8, 475 Seiten

Reihe: COURSE OF THEORETICAL PHYSICS

Covers the theory of electromagnetic fields in matter, and the theory of the macroscopic electric and magnetic properties of matter. There is a considerable amount of new material particularly on the theory of the magnetic properties of matter and the theory of optical phenomena with new chapters on spatial dispersion and non-linear optics. The chapters on ferromagnetism and antiferromagnetism and on magnetohydrodynamics have been substantially enlarged and eight other chapters have additional sections.

Autoren/Hrsg.

Landau, L D

Bell, J. S.

Kearsley, M. J.

Pitaevskii, L. P.

Lifshitz, E. M.

Sykes, J. B.

Inhaltsverzeichnis

1;Front Cover;1
2;Electrodynamics of Continuous Media;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE TO THE SECOND EDITION;10
6;PREFACE TO THE FIRST ENGLISH EDITION;12
7;NOTATION;13
8;CHAPTER I. ELECTROSTATICS OF CONDUCTORS;16
8.1;§1. The electrostatic field of conductors;16
8.2;§2. The energy of the electrostatic field of conductors;18
8.3;§3. Methods of solving problems in electrostatics;23
8.4;§4. A conducting ellipsoid;34
8.5;§5. The forces on a conductor;44
8.6;PROBLEMS;47
9;CHAPTER II. ELECTROSTATICS OF DIELECTRICS;49
9.1;§6. The electric field in dielectrics;49
9.2;§7. The permittivity;50
9.3;§8. A dielectric ellipsoid;54
9.4;§9. The permittivity of a mixture;57
9.5;§10. Thermodynamic relations for dielectrics in an electric field;59
9.6;§12. Electrostriction of isotropic dielectrics;66
9.7;§13. Dielectric properties of crystals;69
9.8;§14. The sign of the dielectric susceptibility;73
9.9;§15. Electric forces in a fluid dielectric;74
9.10;§16. Electric forces in solids;79
9.11;§17. Piezoelectrics;82
9.12;§18. Thermodynamic inequalities;89
9.13;§19. Ferroelectrics;92
9.14;§20. Improper ferroelectrics;98
10;CHAPTER III. STEADY CURRENT;101
10.1;§21. The current density and the conductivity;101
10.2;§22. The Hall effect;105
10.3;§23. The contact potential;107
10.4;§24. The galvanic cell;109
10.5;§25. Electrocapillarity;111
10.6;§26. Thermoelectric phenomena;112
10.7;§27. Thermogalvanomagnetic phenomena;116
10.8;§28. Diffusion phenomena;117
11;CHAPTER IV. STATIC MAGNETIC FIELD;120
11.1;§29. Static magnetic field;120
11.2;§30. The magnetic field of a steady current;122
11.3;§31. Thermodynamic relations in a magnetic field;128
11.4;§32. The total free energy of a magnetic substance;131
11.5;§33. The energy of a system of currents;133
11.6;§34. The self-inductance of linear conductors;136
11.7;§35. Forces in a magnetic field;141
11.8;§36. Gyromagnetic phenomena;144
12;CHAPTER V. FERROMAGNETISM AND ANTIFERROMAGNETISM;145
12.1;§37. Magnetic symmetry of crystals;145
12.2;§38. Magnetic classes and space groups;147
12.3;§39. Ferromagnets near the Curie point;150
12.4;§40. The magnetic anisotropy energy;153
12.5;§41. The magnetization curve of ferromagnets;156
12.6;§42. Magnetostriction of ferromagnets;159
12.7;§43. Surface tension of a domain wall;162
12.8;§44. The domain structure of ferromagnets;168
12.9;§45. Single-domain particles;172
12.10;§46. Orientational transitions;174
12.11;§47. Fluctuations in ferromagnets;177
12.12;§48. Antiferromagnets near the Curie point;181
12.13;§49. The bicritical point for an antiferromagnet;185
12.14;§50. Weak ferromagnetism;187
12.15;§51. Piezomagnetism and the magnetoelectric effect;191
12.16;§52. Helicoidal magnetic structures;193
13;CHAPTER VI. SUPERCONDUCTIVITY;195
13.1;§53. The magnetic properties of superconductors;195
13.2;§54. The superconductivity current;197
13.3;§55. The critical field;200
13.4;§56. The intermediate state;204
13.5;§57. Structure of the intermediate state;209
14;CHAPTER VII. QUASI-STATIC ELECTROMAGNETIC FIELD;214
14.1;§58. Equations of the quasi-static field;214
14.2;§59. Depth of penetration of a magnetic field into a conductor;216
14.3;§60. The skin effect;223
14.4;§61. The complex resistance;225
14.5;§62. Capacitance in a quasi-steady current circuit;229
14.6;§63. Motion of a conductor in a magnetic field;232
14.7;§64. Excitation of currents by acceleration;237
14.8;PROBLEMS;238
15;CHAPTER VIII. MAGNETOHYDRODYNAMICS;240
15.1;§65. The equations of motion for a fluid in a magnetic field;240
15.2;§66. Dissipative processes in magnetohydrodynamics;243
15.3;§67. Magnetohydrodynamic flow between parallel planes;245
15.4;§68. Equilibrium configurations;247
15.5;§69. Hvdromagnetic waves;250
15.6;§70. Conditions at discontinuities;255
15.7;§71. Tangential and rotational discontinuities;255
15.8;§72. Shock waves;260
15.9;§73. Evolutionary shock waves;262
15.10;§74. The turbulent dynamo;268
16;CHAPTER IX. THE ELECTROMAGNETIC WAVE EQUATIONS;272
16.1;§75. The field equations in a dielectric in the absence of dispersion;272
16.2;§76. The electrodynamics of moving dielectrics;275
16.3;§77. The dispersion of the permittivity;279
16.4;§78. The permittivity at very high frequencies;282
16.5;§79. The dispersion of the magnetic permeability;283
16.6;§80. The field energy in dispersive media;287
16.7;§81. The stress tensor in dispersive media;291
16.8;§82. The analytical properties of e(.);294
16.9;§83. A plane monochromatic wave;298
16.10;§84. Transparent media;301
16.11;PROBLEM;303
17;CHAPTER X. THE PROPAGATION OF ELECTROMAGNETIC WAVES;305
17.1;§85. Geometrical optics;305
17.2;§86. Reflection and refraction of electromagnetic waves;308
17.3;§87. The surface impedance of metals;315
17.4;§88. The propagation of waves in an inhomogeneous medium;319
17.5;§89. The reciprocity principle;323
17.6;§90. Electromagnetic oscillations in hollow resonators;325
17.7;§91. The propagation of electromagnetic waves in waveguides;328
17.8;§92. The scattering of electromagnetic waves by small particles;334
17.9;§93. The absorption of electromagnetic waves by small particles;337
17.10;§94. Diffraction by a wedge;338
17.11;§95. Diffraction by a plane screen;342
17.12;PROBLEMS;343
18;CHAPTER XI. ELECTROMAGNETIC WAVES IN ANISOTROPIC MEDIA;346
18.1;§96. The permittivity of crystals;346
18.2;§97. A plane wave in an anisotropic medium;348
18.3;§98. Optical properties of uniaxial crystals;354
18.4;§99. Biaxial crystals;356
18.5;§100. Double refraction in an electric field;362
18.6;§101. Magnetic–optical effects;362
18.7;§102. Mechanical–optical effects;370
19;CHAPTER XII. SPATIAL DISPERSION;373
19.1;§103. Spatial dispersion;373
19.2;§104. Natural optical activity;377
19.3;§105. Spatial dispersion in optically inactive media;381
19.4;§106. Spatial dispersion near an absorption line;382
20;CHAPTER XIII. NON-LINEAR OPTICS;387
20.1;§107. Frequency transformation in non-linear media;387
20.2;§108. The non-linear permittivity;389
20.3;§109. Self-focusing;393
20.4;§110. Second-harmonic generation;398
20.5;§111. Strong electromagnetic waves;403
20.6;§112. Stimulated Raman scattering;406
21;CHAPTER XIV. THE PASSAGE OF FAST PARTICLES THROUGH MATTER;409
21.1;§113. Ionization losses by fast particles in matter: the non-relativistic case;409
21.2;§114. Ionization losses by fast particles in matter: the relativistic case;414
21.3;§115. Cherenkov radiation;421
21.4;§116. Transition radiation;423
22;CHAPTER XV. SCATTERING OF ELECTROMAGNETIC WAVES;428
22.1;§117. The general theory of scattering in isotropic media;428
22.2;§118. The principle of detailed balancing applied to scattering;434
22.3;§119. Scattering with small change of frequency;437
22.4;§120. Rayleigh scattering in gases and liquids;443
22.5;§121. Critical opalescence;448
22.6;§122. Scattering in liquid crystals;450
22.7;§123. Scattering in amorphous solids;451
23;CHAPTER XVI. DIFFRACTION OF X-RAYS IN CRYSTALS;454
23.1;§124. The general theory of X-ray diffraction;454
23.2;§125. The integral intensity;460
23.3;§126. Diffuse thermal scattering of X-rays;462
23.4;§127. The temperature dependence of the diffraction cross-section;464
24;APPENDIX: CURVILINEAR COORDINATES;467
25;INDEX;470

Leseproben

CHAPTER I

ELECTROSTATICS OF CONDUCTORS

Publisher Summary

Macroscopic electrodynamics is concerned with the study of electromagnetic fields in space that is occupied by matter. Electrodynamics deals with physical quantities averaged over elements of volume that are physically infinitesimal and ignore the microscopic variations of the quantities that result from the molecular structure of matter. The fundamental equations of the electrodynamics of continuous media are obtained by averaging the equations for the electromagnetic field in a vacuum. The form of the equations of macroscopic electrodynamics and the significance of the quantities appearing in them depend on the physical nature of the medium and on the way in which the field varies with time. Charges present in a conductor must be located on its surface. The presence of charges inside a conductor would cause an electric field in it. These charges can be distributed on its surface, however, in such a way that the fields that they produce in its interior are mutually balanced. The mean field in the vacuum is almost the same as the actual field. The two fields differ only in the immediate neighborhood of the body, where the effect of the irregular molecular fields is noticeable, and this difference does not affect the averaged field equations.

§1 The electrostatic field of conductors

Macroscopic electrodynamics is concerned with the study of electromagnetic fields in space that is occupied by matter. Like all macroscopic theories, electrodynamics deals with physical quantities averaged over elements of volume which are “physically infinitesimal”, ignoring the microscopic variations of the quantities which result from the molecular structure of matter. For example, instead of the actual “microscopic” value of the electric field e, we discuss its averaged value, denoted by E:

¯=E. (1.1)

(1.1)

The fundamental equations of the electrodynamics of continuous media are obtained by averaging the equations for the electromagnetic field in a vacuum. This method of obtaining the macroscopic equations from the microscopic was first used by H. A. Lorentz (1902).

The form of the equations of macroscopic electrodynamics and the significance of the quantities appearing in them depend essentially on the physical nature of the medium, and on the way in which the field varies with time. It is therefore reasonable to derive and investigate these equations separately for each type of physical object.

It is well known that all bodies can be divided, as regards their electric properties, into two classes, and , differing in that any electric field causes in a conductor, but not in a dielectric, the motion of charges, i.e. an †

Let us begin by studying the static electric fields produced by charged conductors, that is, the First of all, it follows from the fundamental property of conductors that, in the electrostatic case, the electric field inside a conductor must be zero. For a field E which was not zero would cause a current; the propagation of a current in a conductor involves a dissipation of energy, and hence cannot occur in a stationary state (with no external sources of energy).

Hence it follows, in turn, that any charges in a conductor must be located on its surface. The presence of charges inside a conductor would necessarily cause an electric field in it;‡ they can be distributed on its surface, however, in such a way that the fields which they produce in its interior are mutually balanced.

Thus the problem of the electrostatics of conductors amounts to determining the electric field in the vacuum outside the conductors and the distribution of charges on their surfaces.

At any point far from the surface of the body, the mean field E in the vacuum is almost the same as the actual field e. The two fields differ only in the immediate neighbourhood of the body, where the effect of the irregular molecular fields is noticeable, and this difference does not affect the averaged field equations. The exact microscopic Maxwell’s equations in the vacuum are

?e=0. (1.2)

(1.2)

?e=-(1/c)?h/?t, (1.3)

(1.3)

where h is the microscopic magnetic field. Since the mean magnetic field is assumed to be zero, the derivative ?h/? also vanishes on averaging, and we find that the static electric field in the vacuum satisfies the usual equations

?E=0,curl?E=0, (1.4)

(1.4)

i.e. it is a potential field with a potential ? such that

=-grad?, (1.5)

(1.5)

and ? satisfies Laplace’s equation

?=0. (1.6)

(1.6)

The boundary conditions on the field E at the surface of a conductor follow from the equation curl E = 0, which, like the original equation (1.3), is valid both outside and inside the body. Let us take the -axis in the direction of the normal n to the surface at some point on the conductor. The component of the field takes very large values in the immediate neighbourhood of the surface (because there is a finite potential difference over a very small distance). This large field pertains to the surface itself and depends on the physical properties of the surface, but is not involved in our electrostatic problem, because it falls off over distances comparable with the distances between atoms. It is important to note, however, that, if the surface is homogeneous, the derivatives ?/, ?/? along the surface remain finite, even though itself becomes very large. Hence, since (curl E) = ?? ?/? = 0, we find that ?? is finite. This means that is continuous at the surface, since a discontinuity in would mean an infinity of the derivative ?? The same applies to , and since E = 0 inside the conductor, we reach the conclusion that the tangential components of the external field at the surface must be zero:

t=0. (1.7)

(1.7)

Thus the electrostatic field must be normal to the surface of the conductor at every point. Since E = - grad ?, this means that the field potential must be constant on the surface of any particular conductor. In other words, the surface of a homogeneous conductor is an equipotential surface of the electrostatic field.

The component of the field normal to the surface is very simply related to the charge density on the surface. The relation is obtained from the general electrostatic equation div e = 4, which on averaging gives

?E=4p?¯, (1.8)

(1.8)

being the mean charge density. The meaning of the integrated form of this equation is well known: the flux of the electric field through a closed surface is equal to the total charge inside that surface, multiplied by 4 Applying this theorem to a volume element lying between two infinitesimally close unit areas, one on each side of the surface of the conductor, and using the fact that E = 0 on the inner area, we find that 4, where s is the surface charge density, i.e. the charge per unit area of the surface of the conductor. Thus the distribution of charges over the surface of the conductor is given by the formula

ps=En=-??/?n, (1.9)

(1.9)

the derivative of the potential being taken along the outward normal to the surface. The total charge on the conductor is

=-14p????ndf, (1.10)

(1.10)

the integral being taken over the whole surface.

The potential distribution in the electrostatic field has the following remarkable property: the function ?() can take maximum and minimum values only at boundaries of regions where there is a field. This theorem can also be formulated thus: a test charge introduced into the field cannot be in stable equilibrium, since there is no point at which its potential energy would have a minimum.

The proof of the theorem is very simple. Let us suppose, for example, that the potential has a maximum at some point not on the boundary of a region where there is a field. Then the point can be surrounded by a small closed surface on which the normal derivative ?? 0 everywhere. Consequently, the integral over this surface (???) d 0. But by...