ELECTRODYNAMICS OF CONTINUOUS MEDIA
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1 ELECTRODYNAMICS OF CONTINUOUS MEDIA by L. D. LANDAU and E. M. LIFSHITZ Institute of Physical Problems, USSR Academy of Sciences Volume 8 of Course of Theoretical Physics Translated from the Russian by J. B. SYKES, J. S. BELL and M. J. KEARSLEY Second Edition revised and enlarged by E. M. LIFSHITZ and L. P. PITAEVSKII PERGAMON PRESS OXFORD NEW YORK SEOUL TOKYO
2 CONTENTS Preface to the second edition Preface to the first English edition Notation ix xi xii I. ELECTROSTATICS OF CONDUCTORS 1. The electrostatic field of conductors 2. The energy of the electrostatic field of conductors Methods of solving problems in electrostatics 4. A conducting ellipsoid The forces on a conductor 29 II. ELECTROSTATICS OF DIELECTRICS 6. The electric field in dielectrics The permittivity 8. A dielectric ellipsoid The permittivity of a mixture 10. Thermodynamic relations for dielectrics in an electric field The total free energy of a dielectric Electrostriction of isotropic dielectrics Dielectric properties of crystals The sign of the dielectric susceptibility Electric forces in a fluid dielectric Electric forces in solids Piezoelectrics 18. Thermodynamic inequalities Ferroelectrics 20. Improper ferroelectrics III. STEADY CURRENT 21. The current density and the conductivity The Hall effect The contact potential The galvanic cell Electrocapillarity 26. Thermoelectric phenomena ThermogalvanomagnetiC phenomena 28. Diffusion phenomena IV. STATIC MAGNETIC FIELD 29. Static magnetic field The magnetic field of a steady current Thermodynamic relations in a magnetic field The total free energy of a magnetic substance 33. The energy of a system of currents
3 vi Contents 34. The self-inductance of linear conductors Forces in a magnetic 36. Gyromagnetic phenomena field V. FERROMAGNETISM AND ANTIFERROMAGNETISM 37. Magnetic symmetry of crystals Magnetic classes and space groups 39. Ferromagnets near the Curie point The magnetic anisotropy energy The magnetization curve of ferromagnets 42. Magnetostriction of ferromagnets Surface tension of a domain wall The domain structure of ferromagnets Single-domain particles Orientational transitions Fluctuations in ferromagnets Antiferromagnets near the Curie point 49. The bicritical point for an antiferromagnet Weak ferromagnetism 51. Piezomagnetism and the magnetoelectric effect Helicoidal magnetic structures 178 VI. SUPERCONDUCTIVITY 53. The magnetic properties of superconductors The superconductivity current 55. The critical field The intermediate state 57. Structure of the intermediate state VII. QUASI-STATIC ELECTROMAGNETIC FIELD 58. Equations of the quasi-static field Depth of penetration of a magnetic field into a conductor The skin effect The complex resistance Capacitance in a quasi-steady current circuit Motion of a conductor in a magnetic field Excitation of currents by acceleration 222 VIII. MAGNETOHYDRODYNAMICS 65. The equations of motion for a fluid in a magnetic field Dissipative processes in magnetohydrodynamics Magnetohydrodynamic flow between parallel planes 68. Equilibrium configurations Hydromagnetic waves 70. Conditions at discontinuities Tangential and rotational discontinuities Shock waves Evolutionary shock waves The turbulent dynamo 253 IX. THE ELECTROMAGNETIC WAVE EQUATIONS 75. The field equations in a dielectric in the absence of dispersion The electrodynamics of moving dielectrics The dispersion of the permittivity 264
4 Contents 78. The permittivity at very high frequencies The dispersion of the magnetic permeability 80. The field energy in dispersive media The stress tensor in dispersive media The analytical properties of e(w) A plane monochromatic wave Transparent media 286 X. THE PROPAGATION OF ELECTROMAGNETIC WAVES 85. Geometrical optics Reflection and refraction of electromagnetic waves The surface impedance of metals The propagation of waves in an inhomogeneous medium The reciprocity principle Electromagnetic oscillations in hollow resonators 91. The propagation of electromagnetic waves in waveguides The scattering of electromagnetic waves by small particles The absorption of electromagnetic waves by small particles Diffraction by a wedge 95. Diffraction by a plane screen XI. ELECTROMAGNETIC WAVES IN ANISOTROPIC MEDIA 96. The permittivity of crystals 97. A plane wave in an anisotropic medium Optical properties of uniaxial crystals Biaxial crystals 100. Double refraction in an electric field Magnetic-optical effects Mechanical-optical effects 355 XII. SPATIAL DISPERSION 103. Spatial dispersion 104. Natural optical activity Spatial dispersion in optically inactive media 106. Spatial dispersion near an absorption line XIII. NON-LINEAR OPTICS 107. Frequency transformation in non-linear media 108. The non-linear permittivity Self-focusing 110. Second-harmonic generation Strong electromagnetic waves Stimulated Raman scattering 391 XIV. THE PASSAGE OF FAST PARTICLES THROUGH MATTER 113. Ionization losses by fast particles in matter: the non-relativistic case 114. Ionization losses by fast particles in matter: the relativistic case Cherenkov radiation Transition radiation 408 XV. SCATTERING OF ELECTROMAGNETIC WAVES 117. The general theory of scattering in isotropic media The principle of detailed balancing applied to scattering Scattering with small change of frequency 422 Vll
5 viii Contents 120. Rayleigh scattering in gases and liquids Critical opalescence Scattering in liquid crystals Scattering in amorphous solids 436 XVI. DIFFRACTION OF X-RAYS IN CRYSTALS 124. The general theory of X-ray diffraction The integral intensity Diffuse thermal scattering of X-rays The temperature dependence of the diffraction cross-section 449 Appendix 452 Index 455
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