The present book is intended for persons acquainted with differential and integral calculus and with vector algebra. The fundamentals of vector analysis are set out in the text as needed. The main object of this book is to find out the physical meaning and content of the fundamental laws and postulates of the theory of electricity. In comparison with this object, only a subordinate part is relegated to formal and logical harmony, and to a strict and ordered treatment.Not trying to achieve completeness of discussion, I omitted even comparatively important questions if they dropped out of the general line of the exposition (for example, thermoelectric phenomena and electrolysis). On the other hand, I permitted myself to treat in somewhat greater detail than is usually the custom some questions (for example in the theory of dielectrics and magnetics). I did not set out technical applications of the theory, but tried as far as possible to prepare the reader to pass over directly to studying the applied theory of electricity.The book was translated from the Russian by G. Leib and was first published by Mir Publishers in 1979. This is the translation of the Ninth Edition of the book.ContentsPreface to the Ninth Russian Edition 11From the Preface to the First Russian Edition 12From the Preface to the Third Russian Edition 13From the Preface to the Eighth Russian Edition 14List of Most Important Symbols 15Introduction 191.Electric Field of Fixed Charges in the Absence of Dielectrics 231.1. Coulomb's Law 231.2. Electric Field 271.3. Gauss's Law 291.4. Electric Field of Charged Surfaces 331.5. Conductors in an Electric Field 381.6. Sources of an Electric Field. Surface Divergence 411.7. Work of Electric Forces. Its Independence of the Shape of thePath. Continuity of the Tangential Components of the Vector E 451.8. Potential of an Electrostatic Field 501.9. Capacitance. Capacitors 561.10. Gradient of Electrostatic Potential. Lines of Force 601.11. Poisson and Laplace Equations 651.12. Potential of Space and Surface Charges 701.13. Typical Problems of Electrostatics 771.14. Electrical Double Layer 811.15. Energy of Interaction of Electric Charges 861.16. Energy of an Electric Field 901.17. Ponderomotive Forces 961.18. Determining the Ponderornotive Forces from the Expression for Energy 991.19. Instability of Electrical Systems. Constraints 1042.Dielectrics 1082.1. Dielectrics. Electric Moment and Potential of a NeutralMolecule. Polarization of a Dielectric 1082.2. Free and Bound Charges. Potential of an Electric Field WhenDielectrics Are Present. Dependence of Polarization on the Field 1132.3. Electric Displacement Vector. Differential Equations of a Fieldin an Arbitrary Medium. Induction Lines 1172.4. Electric Field in a Homogeneous Dielectric 1222.5. Direct Calculation of a Field When a Dielectric Is Present (inVery Simple Cases) 1252.6. Micro- and Macroscopic Values of Physical Quantities 1302.7. Derivation of Equations for the Field in Dielectrics by Averaging theMicroscopic Field 1342.8. Two Classes of Dielectrics. Quasi-Elastic Dipoles 1372.9. Difference of the Field Acting on a Dipole from the Mean One 1392.10. Polarization of Dielectrics Whose Molecules Have a ConstantElectric Moment. Temperature Dependence of Permittivity 1442.11. Energy of the Electric Field in Dielectrics 1502.12. Energy Transformations Connected with the Polarization ofDielectrics. Free Energy of an Electric Field 1542.13. Ponderomotive Forces in Dielectrics 1622.14. Reduction of Body Forces to Tensions 1702.15. Stress Tensor of an Electric Field 1753.Steady Electric Current 1843.1. Current in Metals. Ohm's and Joule's Laws. Voltage 1843.2. Current Density. Differential Form of Ohm's and Joule's Laws 1883.3. Conditions of Steadiness of Currents. ContinuityEquation. Current Filaments 1913.4. Extraneous Electromotive Forces. Quasilinear Currents. Kirchhoff'sSecond Law 1953.5. Conversion of Energy in a Current Circuit. Contact E.M.F.'s 2003.6. Fundamental Concepts of the Electron Theory of Metals. Tolman's Experiments 2063.7. Electron Theory of Electrical Conductivity. Difficulties of theClassical Theory. Sommerfeld's Theory 2104.Ponderomotive Interaction of Steady Currents and Their Magnetic Field(in the Absence of Magnetizing Media) 2184.1. The Magnetic Field of Currents 2184.2. Interaction of Current Elemerits. The Electromagnetic Constant 2224.3. Transition from Line Currents to Currents Having a Finite CrossSection 2264.4. Lorentz Force 2294.5. Vector Potential of a Magnetic Field 2344.6. Differential Equations of a Magnetic Field. Circulation ofMagnetic Field Intensity 2394.7. Potential Fields and Solenoidal Fields. Comparison ofDifferential Equations for an Electric and a Magnetic Fields 2414.8. Boundary Conditions in the Magnetic Field of Currents. SurfaceCurrents. Surface Curl. Field of an Infinite Solenoid 2424.9. Ponderomotive Forces Acting on a Current Loop in a MagneticField. Potential Function of a Current in an External Magnetic Field 2484.10. Ponderomotive Interaction of Currents. Mutual Induction 2524.11. Self-Inductance. Total Potential Function of a System ofCurrents 2584.12. Magnetic Lines of Force 2624.13. Topology of a Vortex (Magnetic) Field. Conditional Barriers 2684.14. Magnetic Sheets. Their Equivalence' to Currents 2724.15. Magnetic Moment of a Current. Elementary Currents and Magnetic Dipoles 2784.16. Direct Determination of the Field of Elementary Currents and theForces Acting on Them 2824.17. Evolution of Notions of the Nature of Magnetism. Spin of Electrons 2904.18. Absolute (Gaussian) and Other Systems of Units, TheElectromagnetic Constant 2945.Magnetics (Magnetizable Media) 3025.1. Magnetization of Magnetics. Molecular Currents and Conduction Currents 3025.2. Vector Potential of a Magnetic Field in the Presence ofMagnetics. Mean Density of Space and Surface Molecular Currents 3065.3. Differential Equations of the Macroscopic Magnetic Field inMagnetics. Magnetic Field Intensity in Magnetics and Magnetic Induction Vector. 3115.4. Dependence of Magnetization on Magnetic Field Intensity. Para-,Dia-, and Ferromagnetics 3145.5. Complete System of Equations for the Field of Steady Currents. Homogeneous Magnetic Medium 3175.6. Mechanical Forces Acting on Currents in a MagneticField. Interaction of Currents 3195.7. Ponderomotive Forces Acting on Magnetics in a Magnetic Field 3235.8. Supplement to the Derivation of the Macroscopic Equations for aMagnetic Field in Magnetics 3255.9. Mechanism of Magnetization of Magnetics. Larmor's Theorem 3295.10. Diamagnetism 3355.11. Paramagnetism 3375.12. More Precise Definitions and Additions to the Theory ofMagnetization. The Part of Spin. Gyromagnetic Phenomena 3435.13. Ferromagnetism. Weiss Molecular Field 3485.14. Equations of the Field in Idealized Ferromagnetics (ConventionalVariant). Permanent Magnets 3565.15. Another Variant of the Equations of the Magnetic Field inIdealized Ferromagnetics. The Equivalence of Electric Currents andPermanent Magnets 3625.16. Ponderomotive Forces Acting on Permanent Magnets in an External Magnetic Field 3716.Quasistationary Electromagnetic Field 3776.1. Induction of Currents in Moving Conductors 3776.2. Law of Electromagnetic Induction. Ohm's Law for Varying Currents 3826.3. Quasistationary Currents. Differential Equations for VaryingCurrents 3866.4. Transformations of Energy in the Field of VaryingCurrents. Energy of Magnetic Interaction of Currents. Lenz's Law 3896.5. Simple Applications of the Varying Current Theory. Transformer 3956.6. Energy of a Magnetic Field. Energy Meaning of Inductances 4036.7. Transformation of Energy in the Magnetization of Para- and Diamagnetics.Free Energy of a Magnetic Field 4116.8. Determination of the Ponderomotive Forces of a Magnetic Fieldfrom the Expression for Energy 4156.9. Stress Tensor of a Magnetic Field 4216.10. Vortices of an Electric Field 4246.11. Dependence of Electric Voltage on Integration Path. Voltage of Alternating Current 4276.12. Equation of Continuity 4326.13. Displacement Currents 4346.14. A Capacitor in the Circuit of a Quasistationary Current. Electric Oscillations 4416.15. The Skin Effect 4467.Varying Electromagnetic Field in a Stationary Medium and ItsPropagation. Electromagnetic Waves 4557.1. System of Maxwell's Equations for Macroscopic Electromagnetic Field. 4557.2. Poynting's Theorem. Energy Flow 4617.3. Unambiguity of the Solutions of Maxwell's Equations 4677.4. Differential Equations for the Potentials of an Electromagnetic Field 4707.5. Solution of the Wave Equation and the d'Alembert Equation 4747.6. Delayed and Advanced Potentials. Gauge Invariance 4817.7. Velocity of Propagation of Electromagnetic Disturbances. Conditions for a Quasistationary State 4887.8. Oscillator. Delayed Potentials of an Oscillator Field 4927.9. Field of an Oscillator. Its Radiation 5017.10. Electromagnetic Nature of Light. Plane Waves in a Dielectric 5137.11. Reflection and Refraction of Plane Waves in Dielectrics 5187.12. Propagation of Waves in a Conducting Medium. Reflection of Lightfrom a Metal Surface 5277.13. Light Pressure. Momentum of an Electromagnetic Field 5327.14. Electromagnetic Angular Momentum. A Particular Case of a StaticField 5397.15. Stress Tensor and Ponderomotive Forces of an ElectromagneticField 5437.16. An Example of Non-Quasistationary Currents: Waves along a Cable 5497.17. Approximate Theory of Fast-Varying Currents. "Telegraph Equation" 5597.18. Free Energy of Ferromagnetics. Hysteresis 5647.19. General Characteristic of the Theories of Short-Range andLong-Range Interaction 5718.Electromagnetic Phenomena in Slowly Moving Media 5768.1. Differential Equations of a Field in Moving Media 5768.2. Convection Current. Polarization and Magnetization of MovingMedia 5818.3. Ohm's Law and Electromagnetic Induction in Moving Conductors. Unipolar Induction 5888.4. A Dielectric Moving in an Electromagnetic Field 5958.5. Propagation of Light in Moving Dielectrics. Fresnel DragCoefficient. Reflection from a Moving Mirror 5978.6. Transformations of Frame of Reference. Relative Nature ofDifference Between Electric and Magnetic Fields 6029.Appendix. Vector Analysis 608A.1. Vector Algebra 608A.2. Vector and Scalar Fields. Gradient 610A.3. Vector Flux Through a Surface 616A.4. Gauss's Theorem. Divergence 619A.5. Circulation of a Vector. Curl of a Vector. Stokes's Theorem 626A.6. Derivative of a Vector with Respect to Direction 634A.7. The Nabla. Second Derivatives. Derivatives of a Product 635A.8. Integral Relationships. Green's Theorem 642A.9. The Most Important Formulas of Vector Analysis 645Fundamental Formulas in the SI and Gaussian Systems of Units 648Supplements 651S.1. Superconductivity (to Sec. 3.7) 651S.2. Antiferromagnetism and Ferrites (to Sec. 5.12) 651S.3. Dispersive Media. Spatial Dispersion (to Sec. 7.2) 652S.4. Anisotropic Media (to Sec. 7.2) 653S.5. Vavilov-Cerenkov Effect (to Sec. 7.9) 654S.6. Plasma (to Sec. 7.12) 654Solutions of Problems 657Name Index 673Subject Index 674