Electrodynamics (eBook)

Front Cover 1
Electrodynamics: Lectures on Theoretical Physics 4
Copyright Page 5
Table of Contents 10
Preface 6
Translator's Note 9
PART I: FUNDAMENTALS AND BASIC PRINCIPLES OF MAXWELL'S ELECTRODYNAMICS 16
Chapter 1. Historical Review. Action at a Distance and Action by a Field 16
Biographical Notes 18
Chapter 2. Introduction to the Basic Concepts of the Electromagnetic Field 21
Chapter 3. Maxwell's Equations in Integral Form 26
Chapter 4. The Maxwell Equations in Differential Form and the Material Constants of the Theory 33
1. Conductivity and Ohm's Law 35
2. Dielectric Constant 36
3. Permeability 36
Chapter 5. Law of Conservation of Energy and Poynting Vector 40
Chapter 6. The Role of the Velocity of Light in Electrodynamics 47
Chapter 7. The Coulomb Field and the Fundamental Constants of Vacuum. Rational and Conventional Units 52
A. Electrostatics 53
B. Magnetostatics 55
C. Rational and Conventional Units 57
D. Final Determination of the Fundamental Constants e0, µ0, MO in the MKSQ System 58
Chapter 8. Four, Five, or Three Fundamental Units? 60
A. Supplementary Note on Our System of Four Units 60
B. The Five Units MKSQP 62
C. The Gaussian System of Only Three Units 64
D. Supplement Regarding Other Systems of Units 68
PART II: DERIVATION OF THE PHENOMENA FROM THE MAXWELL EQUATIONS 70
Chapter 9. The Simplest Boundary-Value Problems of Electrostatics 70
A. Charging Problems 70
B. Induction Problems and Method of Reciprocal Radii 71
C. Conducting Sphere in a Uniform Field 73
D. Dielectric Sphere in a Uniform Field 75
E. Reflection and Refraction of Lines of Force at the Boundary of a Semiinfinite Dielectric 78
Chapter 10. Capacity and Its Connection with Field Energy 79
A. The Plate Condenser 80
B. Spherical Condenser 81
C. Capacity of an Ellipsoid of Revolution and of a Straight Piece of Wire 83
D. Energetic Definition of Capacity 83
E. The Capacities in an Arbitrary System of Conductors 85
Chapter 11. General Considerations on the Electric Field 86
A. The Law of Refraction for the Lines of Force 86
B. On the Definition of the Vectors E and D 87
C. The Concept of Electric Polarization the Clausius-Mossotti Formula
D. Supplement to the Calculation of the Polarization 91
E. Permanent Polarization 92
Chapter 12. The Field of the Permanent Bar Magnet 93
Chapter 13. General Considerations on Magnetostatics and Corresponding Boundary- Value Problems 103
A. The Law of Refraction of the Lines of Magnetic Excitation 104
B. Definition of the Vectors H and B, Particularly in Solid Bodies 104
C. The Magnetization M in Any Non-Ferromagnetic Substance 104
D. Dia- and Paramagnetism 105
E. Soft Iron as Analog to the Electric Conductor 106
F. Specific Boundary-Value Problems 106
G. The Uniform Field within an Ellipsoid of Revolution 107
H. The So-Called Demagnetization Factor 110
Chapter 14. Some Remarks on Ferromagnetism 111
A. The Weiss Domains 112
B. The Electron Spin as Elementary Magnet 113
C. Hysteresis Loop and Reversible Magnetization 113
D. Thermodynamics 115
Chapter 15. Stationary Currents and Their Magnetic Field. Method of the Vector Potential 115
A. The Law of Biot-Savart 118
B. The Magnetic Energy of the Field of Two Conductors 119
C. Neumann's Potential as Coefficient of Mutual Induction 121
D. The Coefficient of Selfinduction 123
E. Self inductance of the Two-Wire Line 127
F. General Theorem Regarding Energy Transmission by Stationary Currents 128
Chapter 16. Ampère's Method of the Magnetic Double Layer 129
A. The Magnetic Shell for Linear Conductors 131
B. Magnetic Energy and Magnetic Flux 134
C. Application to the Self inductance of a Two-Wire Line 136
D. Application to the Electromagnetic Current Measurement of Wilhelm Weber 138
Chapter 17. Detailed Treatment of the Field of a Straight Wire and of a Coil 140
Chapter 18. Quasi-Stationary Currents 148
A. Energetic Interpretation of the Wave Equation 150
B. The Wheatstone Bridge 155
C. Coupled Circuits 157
D. The Telegraph Equation 158
Chapter 19. Rapidty Variable Fields. The Electrodynamic Potentials 160
A. The Retarded Potentials 162
B. The Hertzian Dipole 163
C. Specialization for Periodic Processes 167
D. The Characteristic Vibrations of a Metallic Spherical Oscillator 169
E. Application to the Theory of X-Rays 170
Chapter 20. General Considerations on the Structure of Wave Fields of Cylindrical Symmetry. Details on Alternating Current Impedance and Skin Effect 171
A. Longitudinal and Transverse Components 172
B. The Wave Field of Semiinfinite Space and Its Skin Effect 175
C. The Alternating Current Impedance of a Semiinfinite Space 178
D. The Rayleigh Resistance of a Wire 181
E. The Alternating Current Inductance 182
F. Further Treatment of the Alternating Current Field of a Circularly Cylindrical Wire 183
Chapter 21. The Alternating-Current Conducting Coil 185
A. The Field of the Coil 185
B. Resistance and Inner Inductive Reactance of the Coil 188
C. The Multilayer Coil 190
Chapter 22. The Problem of Waves on Wires 192
A. The Field within and outside of the Wire 193
B. The Boundary Condition at Infinity 196
C. The Boundary Condition at the Surface of the Wire 197
Chapter 23. General Solution of the Wire-Wave Problem 200
A. Primary Wave and Electrical Secondary Waves 201
B. Magnetic Waves 202
C. Asymmetric Waves of the Electromagnetic Type 203
D. Wire Waves on a Nonconductor 205
Chapter 24. On the Theory of Wave Guides 208
Chapter 25. The Lecher Two-Wire Line 213
A. The Limiting Case of Infinite Conductivity 215
B. The Exterior of the Wires 217
C. The Interior of the Wires 219
D. The Boundary Condition Hv = H 221
E. The Boundary Condition for Ex and the Law of Phase Propagation 221
F. Supplement Regarding the Remaining Boundary Conditions 223
G. Parallel and Push-Pull Operation 224
PART III: THEORY OF RELATIVITY AND ELECTRON THEORY 227
Chapter 26. The Invariance of the Maxwell Equations in the Four-Dimensional World 227
A. The Four-Potential 227
B. The Six-Vectors of Field and Excitation 229
C. The Maxwell Equations in Four-Dimensional Form 231
D. On the Geometric Character of the Six-Vector and Its Invariants 233
E. Relativistically Invariant Three-Vectors 235
Chapter 27. The Group of the Lorentz Transformations and the Kinematics of the Theory of Relativity 237
A. The General and the Special Lorentz Transformation 238
B. The Relative Nature of Time 240
C. The Lorentz Contraction 241
D. The Einstein Dilatation of Time 242
E. The Addition Theorem for the Velocity 244
F. c as Upper Limit for All Velocities 245
G. Light Cone Space-Like Vectors and Time-Like Vectors
H. The Addition Theorem for Velocities of Different Directions 248
J. The Principles of the Constancy of the Velocity of Light and of Charge 249
Chapter 28. Preparation for the Electron Theory 251
A. The Transformation of the Electric Field. Preliminaries Regarding the Lorentz Force 252
B. The Magnetic Analog to the Lorentz Force 253
C. The Intrinsic Field of an Electron in Uniform Motion 254
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 258
Chapter 29. Integration of the Differential Equation of the Four-Potential 260
A. Four-Dimensional Form of the Potential O 261
B. Retarded Potentials 263
C. The Lienard-Wiechert Approximation 264
Chapter 30. The Field of the Accelerated Electron 266
A. Electron in Uniform Motion 267
B. The Accelerated Electron 268
C. The Longitudinally Accelerated Electron 269
Chapter 31. The Maxwell Stresses and the Stress-Energy Tensor 270
Chapter 32. Relativistic Mechanics 277
A. The Equivalence of Energy and Mass 279
B. Relationship between Momentum and Energy 281
C. The Principles of D'Alembert and Hamilton 281
D. The Lagrange Function and Lagrange Equations 283
E. Schwarzschild's Principle of Least Action 284
Chapter 33. Electromagnetic Theory of the Electron 288
PART IV: MAXWELL'S THEORY FOR MOVING BODIES AND OTHER ADDENDA 295
Chapter 34. Minkowski's Equations for Moving Media 295
Chapter 35. The Ponderomotive Forces and the Stress-Energy Tensor 305
Chapter 36. The Energy Loss of the Accelerated Electron by Radiation and Its Reaction on the Motion 308
Chapter 37. Approaches to the Generalization of Maxwell's Equations and to the Theory of the Elementary Particles 316
Chapter 38. General Theory of Relativity Unified Theory of Gravitation and Electrodynamics
A. Gravitational and Inertial Mass 327
B. Observable Deductions from the General Theory of Relativity 330
C. Unified Theory of Gravitation and Electrodynamics 336
SYMBOLS EMPLOYED THROUGHOUT THE TEXT AND THEIR DIMENSIONS 338
ADDITIONAL SYMBOLS IN PARTS III AND IV 339
NUMERICAL VALUES, RESULTS OF MEASUREMENTS, AND DEFINITIONS 341
PROBLEMS FOR PART I 342
1.1. The Boundary Conditions of Maxwell's Theory 342
1.2. The Magnetic Excitation Inside and Outside of an Infinitely Long Wire.. 342
1.3. The Magnetic Excitation within an Infinitely Long Solenoid 342
1.4. The Cosine Law of Spherical Trigonometry as Special Case of a General Vector Formula 342
PROBLEMS FOR PART II 342
II.1. The Charging Potential of a Conducting Ellipsoid of Revolution 342
II.2. The Unilaterally Infinitely Long Rubbed Glass Rod and Its Comparison with the Conducting Paraboloid of Revolution 343
II.3. Comparison of the Dielectric and the Conducting Sphere 343
II.4. Edge Correction for the Plate Condenser According to Kirchhoff 343
II.5. The Capacitance of a Leyden (Cylindrical Condenser) 343
II.6. On the Definition of the Capacitance of Two Conductors with Equal and Opposite Charges 343
II.7. Characteristic Oscillations and Characteristic Frequencies of a Completely Conducting Cavity Bounded by a Rectangular Parallelepiped 345
II.8. Characteristic Oscillations and Characteristic Frequencies of the Interior of a Completely Conducting Circular Cylinder of Finite Length 345
II.9. Characteristic Oscillations within a Cavity Bounded by a Metal Sphere 345
II.10. Determination of the Propagation Constants of Wire Waves from Kelvin's Telegraph Equation and from Rayleigh's Alternating Current Resistance 345
PROBLEMS FOR PARTS III AND IV 345
III.1. The Lorentz Transformation for a Relative Motion Deviating from the x-Axis 345
III.2. On the Addition Theorem for Two Differently Directed Velocities 346
III.3. The Field of an Electron in Uniform Motion 346
III.4. On the Relativistic Energy Theorem for the Electron 346
III.5. The Electron in a Uniform Electrostatic Field 346
III.6. The Electron in a Uniform Magnetostatic Field 346
III.7. The Electron in a Uniform Electric Field and a Uniform Magnetic Field which is Parallel thereto 346
III.8. The Electron in a Uniform Electric Field and a Uniform Magnetic Field Perpendicular thereto 347
III.9. The Characteristic of the Thermionic Diode According to Langmuir and Schottky 347
III.10. The Acceleration of the Electron in the Betatron 348
IV.1. The Field of Unipolar Induction 348
ANSWERS AND COMMENTS 349
AUTHOR INDEX 380
SUBJECT INDEX 382