Table of Contents

Cover

Related Titles

Title Page

Copyright

Preface

Basic Notations

Fundamental Constants and Frequently Used Numbers

Chapter 1: Equations of Steady Electric and Magnetic Fields in Media

1.1 Averaging Microscopic Maxwell Equations. Vectors of Electromagnetic Fields in Media

1.2 Equations of Electrostatics and Magnetostatics in Medium

1.3 Polarization of Media in a Constant Field

Problems

1.4 Answers and Solutions

Chapter 2: Electrostatics of Conductors and Dielectrics

2.1 Basic Concepts and Methods of Electrostatics

Problems

2.2 Special Methods of Electrostatics

Problems

2.3 Energy, Forces, and Thermodynamic Relations for Conductors and Dielectrics

Problems

2.4 Answers and Solutions

Chapter 3: Stationary Currents and Magnetic Fields in Media

3.1 Stationary Current

Problems

3.2 Magnetic Field in Magnetic Media

Problems

3.3 Energy, Forces, and Thermodynamic Relations for Magnetics

Problems

3.4 Electric and Magnetic Properties of Superconductors

Problems

Problems

Problems

3.5 Answers and Solutions

Chapter 4: Quasi-Stationary Electromagnetic Field

4.1 Quasi-Stationary Phenomena in Linear Conductors

Problems

4.2 Eddy Currents and Skin-Effect

Problems

4.3 Magnetic Hydrodynamics

Problems

4.4 Answers and Solutions

Chapter 5: Maxwell Equations for Alternating and Inhomogeneous Fields

5.1 Different Forms of Maxwell Equations in Media. Coupling Equations and Electromagnetic Response Functions

Problems

5.2 Causality Principle and Dispersion Relations

Problems

5.3 Energy Relations for Alternating Electromagnetic Field in Media. Longitudinal Electric Oscillations

Problems

5.4 Magnetic Oscillations and Magnetic Resonance

Problems

5.5 Electrodynamics of Moving Media

Problems

Problems

5.6 Energy–Momentum Tensor in Dispersive Media

Problems

5.7 Answers and Solutions

Chapter 6: Propagation of Electromagnetic Waves

6.1 Transverse Waves in Isotropic Media. Reflection and Refraction of Waves

Problems

6.2 Plane Waves in Anisotropic and Gyrotropic Media

Problems

6.3 Scattering of Electromagnetic Waves by Macroscopic Bodies. Diffraction

Problem

Problems

6.4 Diffraction of X-Rays

Problems

6.5 Answers and Solutions

Chapter 7: Coherence and Nonlinear Waves

7.1 Coherence and Interference

Problems

7.2 Random Waves and Waves in Randomly Inhomogeneous Media

Problems

7.3 Waves in Nonlinear and Active Media

Problems

7.4 Answers and Solutions

Chapter 8: Electromagnetic Oscillations in Finite Bodies

8.1 Electromagnetic Waves in Waveguides

Problems

8.2 Electromagnetic Oscillations in Resonators

Problems

8.3 Answers and Solutions

Chapter 9: Interaction of Charged Particles with Equilibrium and Nonequilibrium Media

9.1 Ionization and Radiation Energy Losses of Fast Particles in Media

Problems

9.2 Macroscopic Mechanisms of Radiation of Fast Particles in Media

Problems

9.3 Channeling and Radiation Emitted by Fast Particles in Crystals

Problems

9.4 Acceleration of Particles in Turbulent Plasma Media

Problems

9.5 Answers and Solutions

Bibliography

Index

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 2.15

Figure 2.16

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 5.1

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 6.10

Figure 6.11

Figure 6.12

Figure 6.13

Figure 6.14

Figure 6.15

Figure 6.16

Figure 6.17

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Figure 7.6

Figure 7.7

Figure 7.8

Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12

Figure 7.13

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4

Figure 8.5

Figure 8.6

Figure 8.7

Figure 8.8

Figure 8.9

Figure 8.10

Figure 8.11

Figure 8.12

Figure 9.1

Figure 9.2

Figure 9.3

Figure 9.4

Figure 9.5

Figure 9.6

Figure 9.7

Figure 9.8

Figure 9.9

Figure 9.10

Figure 9.11

Figure 9.12

Figure 9.16

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Igor N. Toptygin

Electromagnetic Phenomena in Matter

Statistical and Quantum Approaches

The Author

Prof. Dr. Igor N. Toptygin

State Polytechnic University

Dept. of Theoretical Physics

St. Petersburg, Russia

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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Preface

This book presents the foundations of macroscopic electrodynamics, namely, the electromagnetic processes in matter and, particularly, the electric and magnetic properties of natural and artificial materials. Due to this feature, it differs essentially from the preceding manual of the same author: “Foundations of Classical and Quantum Electrodynamics,” Wiley-VCH, 2014, which is devoted to electrodynamics in vacuum. Both books are closely connected by the common concept and style of presentation. The general peculiarities of the style of the first book are preserved: these are a combination of the brief textbook and detailed collection of problems; a wide range of examples that are offered to a reader for comprehensive study to stimulate the creative activity; a consideration of the material of various complexity for both the bachelor and master level preparations and also for the extension of knowledge and skills of research engineers and young scientific fellows.

In this edition, like in the first one, the more complicated problems are indicated by asterisks and the most difficult problems by double asterisks. In addition, the bullet is used to mark the problems concerning general and important concepts. It is recommended that these problems are solved first. The number of problems in each chapter significantly exceeds the necessary minimum for adoption of the presented subject, and the reader may solve only part of them and/or study the methods of solution considered in the book, depending on the scope of interests or professional level.

Macroscopic electrodynamics finds its numerous and versatile applications in statistical physics, solid state physics, astrophysics and geophysics, theory of electromagnetic wave propagation, theory of the interaction of charged particles with various media and in many other fields of science. As for applications of macroscopic electrodynamics in the areas of industry and technology, they are almost unlimited. Along with the presentation of general regularities, the author has attempted to give attention to the issues of application of electrodynamics in the neighboring fields to the extent permissible for text books of general purpose. All the examples and many problems are analyzed in great detail. This will allow the user to make use of the knowledge and skills obtained through the work on the book for solving similar problems.

Though the main laws of electromagnetism were formulated in its contemporary form even as early as the in the nineteenth century (the Maxwell equations), most of their applications in the interdisciplinary sciences, especially those concerning the structure of matter, were carried out sometime later, in the twentieth century. These applications were based not only on the laws of electromagnetism but also substantially on the two fundamental theories, developed early in the twentieth century, namely, theory of relativity and quantum mechanics, which proved their fruitfulness in the past decades. The author has tried to present the main results ofthese profound achievements, using his experience in scientific research and in lecturing the course of theoretical physics at St. Petersburg State Polytechnic University (SPbSPU, the former Leningrad Polytechnic Institute). The founders of theoretical studies at SPbSPU are well-known scientists: A.A. Friedman, V.R. Bursian, V.K. Frederiks, Ya.I. Frenkel and others. A significant role in the development of the incipient theoretical physics in St. Petersburg has been played by Paul Erenfest.

The specific character of the book is adequately reflected in its contents. The reader should keep in mind that the most fundamental laws are considered in Chapters 1 and 5, which by no means could be omitted in studying the book. The mathematical formalism of electrodynamics is briefly presented in Chapter 1 of the book “Foundations of Classical and Quantum Electrodynamics,” which is numerously cited in the present edition (specifically in the context of mathematical basis). These references are indicated by a Roman “I,” for example, (I.2.142) denotes the reference to Equation 142 from Chapter 2 of “Foundations…” Other chapters of the present book contain the most important, and in many cases, nontrivial applications of electrodynamics in the contiguous fields such as ferroelectrics (Chapter 2), ferromagnetics and superconductivity (Chapter 3), magnetic hydrodynamics including turbulent state (Chapter 4), nonlinear waves (Chapter 7), and others. They could be read at random, depending on the interest of the reader.

Initially, the proposed book has been published by “Regular and Chaotic Dynamics” Press in 2005 in Russian as a second volume of the two-volume course under the general name “Contemporary Electrodynamics.” As compared with the Russian edition, this book contains more up-to-date material. Chapter 5 is supplemented by the section “Energy-momentum tensor in dispersive media.” Chapter 6 offers the information on meta-materials, on cloaking of material bodies by electromagnetic waves, on waves in the gyrotropic media.

The English translation of this book became possible thanks to the grant of the Russian Ministry of Education and Science (project 11. G34.31.0001) and the project 5–100–2020 of Saint-Petersburg State Polytechnical University in Russia. I greatly appreciate the assistance of my colleagues from the A.F. Ioffe Physical Technical Institute and from Saint-Petersburg State Polytechnical University: A.M. Bykov, A.M. Krassilchtchikov, D.A. Varshalovich, D.G. Yakovlev, D.V. Kupriyanov, V.V. Dubov, A.I. Borovkov (vice-rector of SPbSPU), S.B. Makarov (director of Institute of Physics of SPbSPU). I am grateful to the translators of the book – Arseny and Elena Berezins, and also to D.G. Yakovlev, scientific editor of English translation of this book. Special thanks are due to Master A. Egorov for drawing a large number of figures. Undergraduate student K. Levina has checked up answers to some problems and also has helped with proof-reading.

Saint Petersburg
June 2014

Igor N. Toptygin

Basic Notations

A | work
f02-math-0001 | vector potential.
f02-math-0002 | Bohr radius.
a, b | constants of crystal lattice.
f02-math-0003 | vector of a reciprocal lattice.
f02-math-0004 | creation and annihilation operators for Dirac particles.
f02-math-0005 | creation and annihilation operators for Dirac antiparticles.
f02-math-0006 | magnetic induction.
c | light velocity in vacuum (limiting velocity).
f02-math-0007 | sound velocity.
C | electric capacity; thermal capacity.
f02-math-0008 | capacity coefficients.
f02-math-0009 | creation and annihilation operators for photons.
f02-math-0010 | diffusion coefficient in momentum space.
f02-math-0011 | electric induction.
f02-math-0012 | electric dipole moment.
f02-math-0013 | covariant components of 4-gradient.
f02-math-0014 | charge of particle or macroscopic body.
f02-math-0015 | unit vector.
f02-math-0016 | strength of the electric field.
E, W | energy.
f02-math-0017 | electromotive force (EMF); total energy of relativistic particle.
F | Helmholtz free energy per unit volume.
f02-math-0018 | Helmholtz free energy of all body.
f02-math-0019 | force.
f02-math-0020 | density of force.
f02-math-0021 | 4-tensor of electromagnetic field.
f02-math-0022 | distribution functions.
f02-math-0023 | density of field's momentum.
G | Green's function.
f02-math-0024 | classical Hamiltonian function.
f02-math-0025 | quantum operator Hamiltonian.
f02-math-0026 | strength of the magnetic field.
f02-math-0027 | reduced Planck constant.
f02-math-0028 | 4-tensor of electromagnetic induction.
p, P | pressure.
f02-math-0029 | momentum of particle.
f02-math-0030 | electric quadrupole moment's tensor.
f02-math-0031 | density of surface current.
I | intensity of emission.
f02-math-0032 | current density (volumetric).
J | total current passing through the surface.
K, T | kinetic energy.
f02-math-0033 | tensor of electromagnetic fluctuations in equilibrium system.
f02-math-0034 | wave vector.
L | inductance; length (characteristic scale); Langevin function.
f02-math-0035 | inductance coefficients.
l | length (characteristic scale).
M, m | mass.
f02-math-0036 | magnetic moment.
f02-math-0037 | vectors of magnetic polarization.
f02-math-0038 | magnetic moment of a macroscopic body.
n, N | density of particle's number.
f02-math-0039 | unit normal vector.
N | total number of particles.
f02-math-0040 | isotropic part of distribution function.
P, p | pressure.
f02-math-0041 | vectors of electric polarization.
f02-math-0042 | electric moment of a macroscopic body.
q, Q | charge of a single particle or macroscopic body.
Q | heat.
f02-math-0043 | density of a heat current; momentum change of scattered particle.

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