Fundamentals of The Theory of Electricity

Front Cover
Title Page
Contents
Preface
Preface to the Ninth Russian Edition
From the Preface to the Third Russian Edition
From the Preface to the Eighth Russian Edition
List of Most Important Symbols
Introduction
1. Electric Field of Fixed Charges in the Absence of Dielectrics
1.1 Coulomb's Law
1.2 Electric Field
1.3 Gauss's Law
1.4 Electric Field of Charged Surfaces
1.5 Conductors in an Electric Field
1.6 Sources of an Electric Field. Surface Divergence
1.7 Work of Electric Forces. Its Independence of the Shape of the Path. Continuity of the Tangential Components of the Vector E
1.8 Potential of an Electrostatic Field
1.9 Capacitance. Capacitors
1.10 Gradient of Electrostatic Potential. Lines of Force
1.11 Poisson and Laplace Equations
1.12 Potential of Space and Surface Charges
1.13 Typical Problems of Electrostatics
1.14 Electrical Double Layer
1.15. Energy of Interaction of Electric Charges
1.16 Energy of an Electric Field
1.17 Ponderomotive Forces
1.18 Determining the Ponderomotive Forces from the Expression for Energy
1.19. Instability of Electrical Systems. Constraints
2. Dielectrics
2.1 Dielectrics. Electric Moment and Potential of a Neutral Molecule. Polarization of a Dielectric
2.2 Free and Bound Charges. Potential of an Electric Field When Dielectrics Are Present. Dependence of Polarization on the Field
2.3 Electric Displacement Vector. Differential Equations of a Field in an Arbitrary Medium. Induction Lines
2.4 Electric Field in a Homogeneous Dielectric
2.5 Direct Calculation of a Field When a Dielectric Is Present (in Very Simple Cases)
2.6 Micro- and Macroscopic Values of Physical Quantities
2.7 Derivation of Equations for the Field in Dielectrics by Averaging the Microscopic Field
2.8 Two Classes of Dielectrics. Quasi-Elastic Dipoles
2.9 Difference of the Field Acting on a Dipole from the Mean One
2.10 Polarization of Dielectrics Whose Molecules Have a Constant Electric Moment. Temperature Dependence of Permittivity
2.11 Energy of the Electric Field in Dielectrics
2.12 Energy Transformations Connected with the Polarization of Dielectrics. Free Energy of an Electric Field
2.13 Ponderomotive Forces in Dielectrics
2.14 Reduction of Body. Forces to Tensions
2.15 Stress Tensor of an Electric Field
3. Steady Electric Current
3.1 Current in Metals. Ohm's and Joule's Laws. Voltage
3.2 Current Density. Differential Form of Ohm's and Joule's Laws
3.3 Conditions of Steadiness of Currents. Continuity Equation. Current Filaments
3.4 Extraneous Electromotive Forces. Quasilinear Currents. Kirchhoff's Second Law
3.5 Conversion of Energy in a Current Circuit. Contact E.M.F.'s
3.6 Fundamental Concepts of the Electron Theory of Metals. Tolman's Experiments
3.7 Electron Theory of Electrical Conductivity. Difficulties of the Classical Theory. Sommerfeld's Theory
4. Ponderomotive Interaction of Steady Currents and Their Magnetic Field (in the Absence of Magnetizing Media)
4.1 The Magnetic Field of Currents
4.2 Interaction of Current Elements. The Electromagnetic Constant
4.3 Transition from Line Currents to Currents Having a Finite Cross Section
4.4 Lorentz Force
4.5 Vector Potential of a Magnetic Field
4.6 Differential Equations of a Magnetic Field. Circulation of Magnetic Field Intensity
4.7 Potential Fields and Solenoidal Fields. Comparison of Differential Equations for an Electric and a Magnetic Fields
4.8 Boundary Conditions in the Magnetic Field of Currents. Surface Currents. Surface Curl. Field of an Infinite Solenoid
4.9 Ponderomotive Forces Acting on a Current Loop in a Magnetic Field. Potential Function of a Current in an External Magnetic Field
4.10 Ponderomotive Interaction of Currents. Mutual Induction
4.11 Self-Inductance. Total Potential Function of a System of Currents
4.12 Magnetic Lines of Force
4.13 Topology of a Vortex (Magnetic) Field. Conditional Barriers
4.14 Magnetic Sheets. Their Equivalence to Currents
4.15 Magnetic Moment of a Current. Elementary Currents and Magnetic Dipoles
4.16 Direct Determination of the Field of Elementary Currents and the Forces Acting on Them
4.17 Evolution of Notions of the Nature of Magnetism. Spin of Electrons
4.18 Absolute (Gaussian) and Other Systems of Units. The Electromagnetic Constant
5. Magnetics (Magnetizable Media)
5.1 Magnetization of Magnetics. Molecular Currents and Conduction Currents
5.2 Vector Potential of a Magnetic Field in the Presence of Magnetics. Mean Density of Space and Surface Molecular Currents
5.3 Differential Equations of the Macroscopic Magnetic Field in Magnetics. Magnetic Field Intensity in Magnetics and Magnetic Induction Vector
5.4 Dependence of Magnetization on Magnetic Field Intensity. Para-, Dia-, and Ferromagnetics
5.5 Complete System of Equations for the Field of Steady Currents. Homogeneous Magnetic Medium
5.6 Mechanical Forces Acting on Currents in a Magnetic Field. Interaction of Currents
5.7 Ponderomotive Forces Acting on Magnetics in a Magnetic Field
5.8 Supplement to the Derivation of the Macroscopic Equations for a Magnetic Field in Magnetics.
5.9 Mechanism of Magnetization of Magnetics. Larmor's Theorem
5.10 Diamagnetism
5.11 Paramagnetism
5.12 More Precise Definition-and Additions to the Theory of Magnetization. The Part of Spin. Gyromagnetic Phenomena
5.13 Ferromagnetism. Weiss Molecular Field
5.14 Equations of the Field in Idealized Ferromagnetics (Conventional Variant). Permanent Magnets
5.15 Another Variant of the Equations of the Magnetic Field in Idealized Ferromagnetics. The Equivalence of Electric Currents and Permanent Magnets
5.16 Ponderomotive Forces Acting on Permanent Magnets in an External Magnetic Field
6. Quasistationary Electromagnetic Field
6.1 Induction of Currents in Moving Conductors
6.2 Law of Electromagnetic Induction. Ohm's Law for Varying Currents
6.3 Quasistationary Currents. Differential Equations for Varying Currents
6.4 Transformations of Energy in the Field of Varying Currents. Energy of Magnetic Interaction of Currents. Lenz's Law
6.5 Simple Applications of the Varying Current Theory. Transformer
6.6 Energy of a Magnetic Field. Energy Meaning of Inductances
6.7 Transformation of Energy in the. Magnetization of Para- and Diamagnetics. Free Energy of a Magnetic Field
6.8 Determination of the Ponderometlve Forces of a Magnetic Field from the Expression for Energy
6.9 Stress Tensor of a Magnetic Field
6.10 Vortices of an Electric Field
6.11 Dependence of Electric Voltage on Integration Path, Voltage of Alternating Current
6.12 Equation of Continuity
6.13 Displacement Currents
6.14 A Capacitor in the Circuit of a Quasistationary Current. Electric Oscillations
6.15 The Skin Effect
7. Varying Electromagnetic Field in a Stationary Medium and Its Propagation. Electromagnetic Waves
7.1 System of Maxwell's Equations for Macroscopic Electromagnetic Field
7.2 Poynting's Theorem. Energy Flow
7.3 Unambiguity of the Solutions of Maxwell's Equations
7.4 Differential Equations for the Potentials of an Electromagnetic Field
7.5 Solution of the Wave Equation and the D'Alembert Equation
7.6 Delayed and Advanced Potentials. Gauge Invariance
7.7 Velocity of Propagation of Electromagnetic Disturbances. Conditions for a Quasistationary State
7.8 Oscillator. Delayed Potentials of an Oscillator Field
7.9 Field of an Oscillator. Its Radiation
7.10 Electromagnetic Nature of Light. Plane Waves in a Dielectric
7.11 Reflection and Refraction of Plane Waves in Dielectrics
7.12 Propagation of Waves in a Conducting Medium. Re8ection of Light from a Metal Surface
7.13 Light Pressure. Momentum of an Electromagnetic Field
7.14 Electromagnetic Angular Momentum. A Particular Case of a Static Field
7.15 Stress Tensor and Ponderomotive Forces of an Electromagnetic Field
7.16 An Example of Non-Quasistationary Currents: Waves along a Cable
7.17 Approximate Theory of Fast-Varying Currents. "Telegraph Equation"
7.18 Free Energy of Ferromagnetics. Hysteresis
7.19 General Characteristic of the Theories of Short-Range and Long-Range Interaction
8. Electromagnetic Phenomena in Slowly Moving Media
8.1 Differential Equations of a Field in Moving Media
8.2 Convection Current. Polarization and Magnetization of Moving Media
8.3 Ohm's Law and Electromagnetic Induction in Moving Conductors. Uniploar Induction
8.4 A Dielectric Moving in an Electromagnetic Field
8.5 Propagation of Light in Moving Dielectrics. Fresnel Drag Coefficient. Reflection from a Moving Mirror
8.6 Transformations of Frame of Reference. Relative Nature of Difference Between Electric and Magnetic Fields
9. Appendix
Vector Analysis
A.1Vector Algebra
A.2 Vector and Scalar Fields. Gradient
A.3 Vector Flux Through a Surface
A.4 Gauss's Theorem. Divergence
A.5 Circulation of a Vector. Curl of a Vector. Stokes's Theorem
A.6 Derivative of a Vector with Respect to Direction
A.7 The Nabla. Second Derivatives. Derivatives of a Product
A.8 Integral Relationships. Green's Theorem
A.9 The Most Impor.tant.Formulas of Vector Analysis
Fundamental Formulas in the SI and Gaussian Systems of Units
Supplements
S.1 Superconductivity (to Sec. 3.7)
S.2 Antiferromagnetism and Ferrites
S.3 Dispersive Media. Spatial Dispersion
S.4 Anisotropic Media (to Sec. 7.2)
S.5 Vavilov-CereDkov Effect
S.6 Plasma
Solutions of Problems
Name Index
Subject Index