目錄
Preface
Translator's Note
PART I. FUNDAMENTALS AND BASIC PRINCIPLES OF MAXWELL'S ELECTRODYNAMICS
§1. Historical Review. Action at a Distance and Action by a Field Biographical Notes
Michael Faraday, 1791
James Clerk Maxwell, 1831
Andr? Marie Amp?re, 1775-1836
Heinrich Hertz, 1857-1894
§2. Introduction to the Basic Concepts of the Electromagnetic Field
§3. Maxwell's Equations in Integral Form
§4. The Maxwell Equations in Differential Form and the Material Constants of the Theory
1. Conductivity and Ohm's Law
2. Dielectric Constant
3. Permeability
§5. Law of Conservation of Energy and Poynting Vector
§6. The Role of the Velocity of Light in Electrodynamics
§7. The Coulomb Field and the Fundamental Constants of Vacuum. Rational and Conventional Units
A. Electrostatics
B. Magnetostatics
C. Rational and Conventional Units
D. Final Determination of the Fundamental Constants eo, uo in the MKSQ System
§8. Four, Five, or Three Fundamental Units
A. Supplementary Note on Our System of Four Units
B. The Five Units MKSQP
C. The Gaussian System of Only Three Units
D. Supplement Regarding Other Systems of Units
PART II. DERIVATION OF THE PHENOMENA FROM THE MAXWELL EQUATION
§9. The Simplest Boundary-Value Problems of Electrostatics
A. Charging Problemg
B. Induction Problems and Method of Reciprocal Radii
C. Conducting Sphere in a Uniform Field
D. Dielectric Sphere in a Uniform Field
E. Reflection and Refraction of Lines of Force at the Boundary of a Semi-infinite Dielectric
§10. Capacity and Its Connection with Field Energy
A. The Plate Condenser
B. Spherical Condenser
C. Capacity of an Ellipsoid of Revolution and of a Straight Piece of Wire
D. Energetic Definition of Capacity
E. The Capacities in an Arbitrary System of Conductors
§11. General Considerations on the Electric Field
A. The Law of Refraction for the Lines of Force
B. On the Definition of the Vectors E and D
C. The Concept of Electric Polarization; the Clausius-Mossotti Formula
D. Supplement to the Calculation of the Polarization
E. Permanent Polarization
§12. The Field of the Permanent Bar Magnet
§13. General Considerations on Magnetostatics and Corresponding Boundary- Value Problems
A. The Law of Refraction of the Lines of Magnetic Excitation
B. Definition of the Vectors H and B, Particularly in Solid Bodies
C. The Magnetization M in Any Non-Ferromagnetic Substance
D. Dia- and Paramagnetism
E. Soft Iron as Analog to the Electric Conductor
F. Spccific Boundary-Value Problems
G. The Uniform Field within an Ellipsoid of Revolution
H. The So-Called Demagnetization Factor
§14. Some Remarks on Ferromagnetism
A. The Weiss Domains
B. The Electron Spin as Elementary Magnet
C. Hysteresis Loop and Reversible Magnetization
D. Thermodvnamics
§15. Stationary Currents and Their Magnetic Field. Method of the Vector Po-tential
A. The Law of Biot-Savart
B. The Magnetic Energy of the Field of Two Conductors
C. Neumann's Potential as Coefficient of Mutual Induction
D. The Coefficient of Selfinduction
E. Selfinductance of the Two-Wire Line
F. General Theorem Regarding Energy Transmission by Stationary Cur- rents
§16. Amp?re's Method of the Magnetic Double Layer
A. The Magnetic Shell for Linear Conductors
B. Magnetic Energy and Magnetic Flux
C. Application to the Selfinductance of a Two-Wire Line
D. Application to the Electromagnetic Current Measurement of Wilhelm Weber
§17. Detailed Treatment of the Field of a Straight Wire and of a Coil
§18. Quasi-Stationary Currents
A. Energetic Interpretation of the Wave Equation
a. Free Vibrations
b. Forced Vibrations
B. The Wheatstone Bridge
C. Coupled Cireuits
D. The Telegraph Equation
§19. Rapidly Variable Fields. The Electrodynamic Potentials
A. The Retarded Potentials
B. The Hertzian Dipole
C. Specialization for Periodic Processes
D. The Characteristic Vibrations of a Metallic Spherical Oscillator
E. Application to the Theory of X-Rays
§20. General Considerations on the Structure of Wave Fields of Cylindrical Sym- metry. Details on Alternating Current Impedance and Skin Effect
A. Longitudinal and Trangverse Components
B. The Wave Field of Semiinfinite Space and Its Skin Effect
C. The Alternating Current Impedance of a Semiinfinite Space
D. The Rayleigh Resistance of a Wire
E. The Alternating Current Inductance
F. Further Treatment of the Alternating Current Field of a Circularly Cy-lindrical Wire
§21. The Alternating-Current Conducting Coil
A. The Field of the Coil
B. Resistance and Inner Inductive Reactance of the Coil
C. The Multilayer Coil
§22. The Problem of Waves on Wires
A. The Field within and outside of the Wire
B. The Boundary Condition at Infinity
C. The Boundary Condition at the Surface of the Wire
§23. General Solution of the Wire-Wave Problem
A. Primary Wave and Electrical Secondary Waves
B. Magnetic Waves
C. Asymmetric Waves of the Electromagnetic Type
D. Wire Waves on a Nonconductor
§24. On the Theory of Wave Guides
§25. The Lecher Two-Wire Line
A. The Limiting Case of Infinite Conductivity
B. The Exterior of the Wires
C. The Interior of the Wires
D. The Boundary Condition H, = H
E. The Boundary Condition for E, and the Law of Phase Propagation
F. Supplement Regarding the Remaining Boundary' Conditions
G. Parallel and Push-Pull Operation
PART III. THEORY OF RELATIVITY AND ELECTRON THEORY
§26. The Invariance of the Maxwell Equations in the Four-Dimensional World
A. The Four-Potential
B. The Six-Vectors of Field and Excitation
C. The Maxwell Equations in Four-Dimensional Form
D. On the Geometric Character of the Six-Vector and Its Invariants
E. Relativistically Invariant Three-Vectors
§27. The Group of the Lorentz Transformations and the Kinematics of the Theory of Relativity
A. The General and the Special Lorentz Transformation
B. The Relative Nature of Time
C. The Lorentz Contraction
D. The Einstein Dilatation of Time
E. The Addition Theorem for the Velocity
F. c as Upper Limit for All Velocities
G. Light Cone;Space-Like Vectors and Time-Like Vectors; Intrinsic Time
H. The Addition Theorem for Velocities of Different Directions
J. The Principles of the Constancy of the Velocity of Light and of Charge
§28. Preparation for the Electron Theory
A. The Transformation of the Electric Field. Preliminaries Regarding the Lorentz Force
B. The Magnetic Analog to the Lorentz Force
C. The Intrinsic Field of an Electron in UUniform Motion
D.An Invariant Approach to the Lorentz Force; the Four-Vector of the Force Density
E. The General Orthogonal Transformation of a Tensor of the Second Rank
§29. Integration of the Differential Equation of the Four-Potential
A. Four-Dimensional Form of the Potential a
B. Retarded Potentials
C. The Lienard-Wiechert Approximation
§30. The Field of the Accelerated Electron
A. Electron in Uniform Motion
B. The Accelerated Electron
C. The Longitudinally Accelerated Electron
§31. The Maxwell Stresses and the Stress-Energy Tensor
§32. Relativistic Mechanics
A. The Equivalence of Energy and Mass
B. Relationship betwecn Momentum and E'nergy
C. The Principles of D'Alembert and Hamilton
D. The Lagrange Function and Lagrange Equations
E. Schwarzschild's Principle of Least Action
§33. Electromagnetic Theory of the Electron
PART IV. MAXWELL'B THEORY FOR MOVIXG BOMIES AND OTHER ADDENDA
§34. Minkowski's Equations for Moving Media
§35. The Ponderomotive Forces and the Stress-Energy Tensor
§36. The Energy Loss of the Accelerated Flectron by Radiation and Its Reaction on the Motion
§37. Approaches to the Generalization of Maxwell's Equations and to the Theory of the Elementary Purticles
§38. General Theory of Relativity; Unified Theory of Gravitation and Elec- trodynamics
A. Gravitational and Inertial Mass
B. Observable Deductions from the General Theory of Relativity
C. Unified Theory of Gravitation and Electrodynamics
SYMBOLS EMPLOYED THROUGHOUT THE TEXT AND THEIR DIMENSIONS
ADDITIONAL SYMBOLS IN PARTS III AND IV
NUMERICAL VALUES, RESULTS OF MEASUREMENTS, AND DEFINITIONS
PROBLEMS FOR PART I
I.1. The Boundary Conditions of Maxwell's Theory
I.2. The Magnetic Excitation Inside and Outside of an Infinitely Long Wire
1.3. The Magnetic Excitation within an Infinitely Long Solenoid
I.4. The Coeine Law of Spherical Trigonometry as Special Case of a Gen- eral Vector Formula
PROBLEMS FOR PART II
II.1. The Charging Potential of a Conducting Ellipsoid of Revolution
II.2. The Unilaterally Infinitely Long Rubbed Glass Rod and Its Com- parison with the Conducting Paraboloid of Revolution
II.3. Comparison of the Dielectric and the Conducting Sphere
II.4. Edge Correction for the Plate Condenser According to Kirchhoff
II.5. The Capacitauce of a Leyden Jar (Cylindrical Condenser)
II.6. On the Definition of the Capacitance of Two Conductors with Equal and Opposite Charges
II.7. Characteristic Oscillations and Characteristic Frequencies of a Com- pletely Conducting Cavity Bounded by a Rectangular Parallelepiped
II.8. Characteristic Oscillations and Characteristic Frequencies of the In- terior of a Completely Conducting Circular Cylinder of Finite Length
II.9. Characteristic Oscillations within a Cavity Bounded by a Metal Sphere
II.10. Determination of the Propagation Constants of Wire Waves from Kelvin's Telegraph Equation and from Rayleigh's Alternating Current Resistance
PROBLEMS FOR PARTS III AND IV
III.1. The Lorentz Transformation for a Relative Motion Deviating from the x-Axis
III.2. On the Addition Theorem for Two Differently Directed Velocities
III.3. The Field of an Electron in Uniform Motion
III.4. On the Relativistic Energy Theorem for the Electron
III.5. The Electron in a Uniform Electrostatic Field
III.6. The Electron in a Uniform Magnetostatic Field
III.7. The Electron in a Uniform Electric Field and a Uniform Magnetic Field which is Parallel thereto
III.8. The Electron in a Uniform Electric Field and a Uniform Magnetic Field Perpendicular thereto
III.9. The Characteristic of the Thermionic Diode According to Langmuir and Schottky
III.10. The Acceleration of the Llectron in the Betatron
VOLUME IV: Optics. 1953. Translation in preparation
VOLUME V: Thermodynamics and Statistical Mechanics
VOLUME: VI: Partial Differential Equations in Physics. Translated by Ernst G.Straus
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