Sommerfeld Electrodynamics

Lectures on Theoretical Physics, Vol. 3
1. Auflage 2013
ISBN: 978-1-4832-1429-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 386 Seiten, Web PDF

Electrodynamics: Lectures on Theoretical Physics Volume III covers topics related to electrodynamics. The book discusses the fundamentals and basic principles of Maxwell's electrodynamics; the derivation of the phenomena from the Maxwell equations; and the theory of relativity. The text also describes the electron theory; as well as Maxwell's theory for moving bodies and other addenda. Physicists and people involved in the study of electrodynamics will find the book invaluable.

Autoren/Hrsg.

Sommerfeld, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Electrodynamics: Lectures on Theoretical Physics;4
3;Copyright Page;5
4;Table of Contents;10
5;Preface;6
6;Translator's Note;9
7;PART I: FUNDAMENTALS AND BASIC PRINCIPLES OF MAXWELL'S ELECTRODYNAMICS;16
7.1;Chapter 1. Historical Review. Action at a Distance and Action by a Field;16
7.1.1;Biographical Notes;18
7.2;Chapter 2. Introduction to the Basic Concepts of the Electromagnetic Field;21
7.3;Chapter 3. Maxwell's Equations in Integral Form;26
7.4;Chapter 4. The Maxwell Equations in Differential Form and the Material Constants of the Theory;33
7.4.1;1. Conductivity and Ohm's Law;35
7.4.2;2. Dielectric Constant;36
7.4.3;3. Permeability;36
7.5;Chapter 5. Law of Conservation of Energy and Poynting Vector;40
7.6;Chapter 6. The Role of the Velocity of Light in Electrodynamics;47
7.7;Chapter 7. The Coulomb Field and the Fundamental Constants of Vacuum. Rational and Conventional Units;52
7.7.1;A. Electrostatics;53
7.7.2;B. Magnetostatics;55
7.7.3;C. Rational and Conventional Units;57
7.7.4;D. Final Determination of the Fundamental Constants e0, µ0, MO in the MKSQ System;58
7.8;Chapter 8. Four, Five, or Three Fundamental Units?;60
7.8.1;A. Supplementary Note on Our System of Four Units;60
7.8.2;B. The Five Units MKSQP;62
7.8.3;C. The Gaussian System of Only Three Units;64
7.8.4;D. Supplement Regarding Other Systems of Units;68
8;PART II: DERIVATION OF THE PHENOMENA FROM THE MAXWELL EQUATIONS;70
8.1;Chapter 9. The Simplest Boundary-Value Problems of Electrostatics;70
8.1.1;A. Charging Problems;70
8.1.2;B. Induction Problems and Method of Reciprocal Radii;71
8.1.3;C. Conducting Sphere in a Uniform Field;73
8.1.4;D. Dielectric Sphere in a Uniform Field;75
8.1.5;E. Reflection and Refraction of Lines of Force at the Boundary of a Semiinfinite Dielectric;78
8.2;Chapter 10. Capacity and Its Connection with Field Energy;79
8.2.1;A. The Plate Condenser;80
8.2.2;B. Spherical Condenser;81
8.2.3;C. Capacity of an Ellipsoid of Revolution and of a Straight Piece of Wire;83
8.2.4;D. Energetic Definition of Capacity;83
8.2.5;E. The Capacities in an Arbitrary System of Conductors;85
8.3;Chapter 11. General Considerations on the Electric Field;86
8.3.1;A. The Law of Refraction for the Lines of Force;86
8.3.2;B. On the Definition of the Vectors E and D;87
8.3.3;C. The Concept of Electric Polarization; the Clausius-Mossotti Formula;88
8.3.4;D. Supplement to the Calculation of the Polarization;91
8.3.5;E. Permanent Polarization;92
8.4;Chapter 12. The Field of the Permanent Bar Magnet;93
8.5;Chapter 13. General Considerations on Magnetostatics and Corresponding Boundary- Value Problems;103
8.5.1;A. The Law of Refraction of the Lines of Magnetic Excitation;104
8.5.2;B. Definition of the Vectors H and B, Particularly in Solid Bodies;104
8.5.3;C. The Magnetization M in Any Non-Ferromagnetic Substance;104
8.5.4;D. Dia- and Paramagnetism;105
8.5.5;E. Soft Iron as Analog to the Electric Conductor;106
8.5.6;F. Specific Boundary-Value Problems;106
8.5.7;G. The Uniform Field within an Ellipsoid of Revolution;107
8.5.8;H. The So-Called Demagnetization Factor;110
8.6;Chapter 14. Some Remarks on Ferromagnetism;111
8.6.1;A. The Weiss Domains;112
8.6.2;B. The Electron Spin as Elementary Magnet;113
8.6.3;C. Hysteresis Loop and Reversible Magnetization;113
8.6.4;D. Thermodynamics;115
8.7;Chapter 15. Stationary Currents and Their Magnetic Field. Method of the Vector Potential;115
8.7.1;A. The Law of Biot-Savart;118
8.7.2;B. The Magnetic Energy of the Field of Two Conductors;119
8.7.3;C. Neumann's Potential as Coefficient of Mutual Induction;121
8.7.4;D. The Coefficient of Selfinduction;123
8.7.5;E. Self inductance of the Two-Wire Line;127
8.7.6;F. General Theorem Regarding Energy Transmission by Stationary Currents;128
8.8;Chapter 16. Ampère's Method of the Magnetic Double Layer;129
8.8.1;A. The Magnetic Shell for Linear Conductors;131
8.8.2;B. Magnetic Energy and Magnetic Flux;134
8.8.3;C. Application to the Self inductance of a Two-Wire Line;136
8.8.4;D. Application to the Electromagnetic Current Measurement of Wilhelm Weber;138
8.9;Chapter 17. Detailed Treatment of the Field of a Straight Wire and of a Coil;140
8.10;Chapter 18. Quasi-Stationary Currents;148
8.10.1;A. Energetic Interpretation of the Wave Equation;150
8.10.2;B. The Wheatstone Bridge;155
8.10.3;C. Coupled Circuits;157
8.10.4;D. The Telegraph Equation;158
8.11;Chapter 19. Rapidty Variable Fields. The Electrodynamic Potentials;160
8.11.1;A. The Retarded Potentials;162
8.11.2;B. The Hertzian Dipole;163
8.11.3;C. Specialization for Periodic Processes;167
8.11.4;D. The Characteristic Vibrations of a Metallic Spherical Oscillator;169
8.11.5;E. Application to the Theory of X-Rays;170
8.12;Chapter 20. General Considerations on the Structure of Wave Fields of Cylindrical Symmetry. Details on Alternating Current Impedance and Skin Effect;171
8.12.1;A. Longitudinal and Transverse Components;172
8.12.2;B. The Wave Field of Semiinfinite Space and Its Skin Effect;175
8.12.3;C. The Alternating Current Impedance of a Semiinfinite Space;178
8.12.4;D. The Rayleigh Resistance of a Wire;181
8.12.5;E. The Alternating Current Inductance;182
8.12.6;F. Further Treatment of the Alternating Current Field of a Circularly Cylindrical Wire;183
8.13;Chapter 21. The Alternating-Current Conducting Coil;185
8.13.1;A. The Field of the Coil;185
8.13.2;B. Resistance and Inner Inductive Reactance of the Coil;188
8.13.3;C. The Multilayer Coil;190
8.14;Chapter 22. The Problem of Waves on Wires;192
8.14.1;A. The Field within and outside of the Wire;193
8.14.2;B. The Boundary Condition at Infinity;196
8.14.3;C. The Boundary Condition at the Surface of the Wire;197
8.15;Chapter 23. General Solution of the Wire-Wave Problem;200
8.15.1;A. Primary Wave and Electrical Secondary Waves;201
8.15.2;B. Magnetic Waves;202
8.15.3;C. Asymmetric Waves of the Electromagnetic Type;203
8.15.4;D. Wire Waves on a Nonconductor;205
8.16;Chapter 24. On the Theory of Wave Guides;208
8.17;Chapter 25. The Lecher Two-Wire Line;213
8.17.1;A. The Limiting Case of Infinite Conductivity;215
8.17.2;B. The Exterior of the Wires;217
8.17.3;C. The Interior of the Wires;219
8.17.4;D. The Boundary Condition Hv = H;221
8.17.5;E. The Boundary Condition for Ex and the Law of Phase Propagation;221
8.17.6;F. Supplement Regarding the Remaining Boundary Conditions;223
8.17.7;G. Parallel and Push-Pull Operation;224
9;PART III: THEORY OF RELATIVITY AND ELECTRON THEORY;227
9.1;Chapter 26. The Invariance of the Maxwell Equations in the Four-Dimensional World;227
9.1.1;A. The Four-Potential;227
9.1.2;B. The Six-Vectors of Field and Excitation;229
9.1.3;C. The Maxwell Equations in Four-Dimensional Form;231
9.1.4;D. On the Geometric Character of the Six-Vector and Its Invariants;233
9.1.5;E. Relativistically Invariant Three-Vectors;235
9.2;Chapter 27. The Group of the Lorentz Transformations and the Kinematics of the Theory of Relativity;237
9.2.1;A. The General and the Special Lorentz Transformation;238
9.2.2;B. The Relative Nature of Time;240
9.2.3;C. The Lorentz Contraction;241
9.2.4;D. The Einstein Dilatation of Time;242
9.2.5;E. The Addition Theorem for the Velocity;244
9.2.6;F. c as Upper Limit for All Velocities;245
9.2.7;G. Light Cone; Space-Like Vectors and Time-Like Vectors; Intrinsic Time;246
9.2.8;H. The Addition Theorem for Velocities of Different Directions;248
9.2.9;J. The Principles of the Constancy of the Velocity of Light and of Charge;249
9.3;Chapter 28. Preparation for the Electron Theory;251
9.3.1;A. The Transformation of the Electric Field. Preliminaries Regarding the Lorentz Force;252
9.3.2;B. The Magnetic Analog to the Lorentz Force;253
9.3.3;C. The Intrinsic Field of an Electron in Uniform Motion;254
9.3.4;D. An Invariant Approach to the Lorentz Force; the Four-Vector of the Force Density;256
9.3.5;E. The General Orthogonal Transformation of a Tensor of the Second Rank;258
9.4;Chapter 29. Integration of the Differential Equation of the Four-Potential;260
9.4.1;A. Four-Dimensional Form of the Potential O;261
9.4.2;B. Retarded Potentials;263
9.4.3;C. The Lienard-Wiechert Approximation;264
9.5;Chapter 30. The Field of the Accelerated Electron;266
9.5.1;A. Electron in Uniform Motion;267
9.5.2;B. The Accelerated Electron;268
9.5.3;C. The Longitudinally Accelerated Electron;269
9.6;Chapter 31. The Maxwell Stresses and the Stress-Energy Tensor;270
9.7;Chapter 32. Relativistic Mechanics;277
9.7.1;A. The Equivalence of Energy and Mass;279
9.7.2;B. Relationship between Momentum and Energy;281
9.7.3;C. The Principles of D'Alembert and Hamilton;281
9.7.4;D. The Lagrange Function and Lagrange Equations;283
9.7.5;E. Schwarzschild's Principle of Least Action;284
9.8;Chapter 33. Electromagnetic Theory of the Electron;288
10;PART IV: MAXWELL'S THEORY FOR MOVING BODIES AND OTHER ADDENDA;295
10.1;Chapter 34. Minkowski's Equations for Moving Media;295
10.2;Chapter 35. The Ponderomotive Forces and the Stress-Energy Tensor;305
10.3;Chapter 36. The Energy Loss of the Accelerated Electron by Radiation and Its Reaction on the Motion;308
10.4;Chapter 37. Approaches to the Generalization of Maxwell's Equations and to the Theory of the Elementary Particles;316
10.5;Chapter 38. General Theory of Relativity; Unified Theory of Gravitation and Electrodynamics;322
10.5.1;A. Gravitational and Inertial Mass;327
10.5.2;B. Observable Deductions from the General Theory of Relativity;330
10.5.3;C. Unified Theory of Gravitation and Electrodynamics;336
11;SYMBOLS EMPLOYED THROUGHOUT THE TEXT AND THEIR DIMENSIONS;338
12;ADDITIONAL SYMBOLS IN PARTS III AND IV;339
13;NUMERICAL VALUES, RESULTS OF MEASUREMENTS, AND DEFINITIONS;341
14;PROBLEMS FOR PART I;342
14.1;1.1. The Boundary Conditions of Maxwell's Theory;342
14.2;1.2. The Magnetic Excitation Inside and Outside of an Infinitely Long Wire..;342
14.3;1.3. The Magnetic Excitation within an Infinitely Long Solenoid;342
14.4;1.4. The Cosine Law of Spherical Trigonometry as Special Case of a General Vector Formula;342
15;PROBLEMS FOR PART II;342
15.1;II.1. The Charging Potential of a Conducting Ellipsoid of Revolution;342
15.2;II.2. The Unilaterally Infinitely Long Rubbed Glass Rod and Its Comparison with the Conducting Paraboloid of Revolution;343
15.3;II.3. Comparison of the Dielectric and the Conducting Sphere;343
15.4;II.4. Edge Correction for the Plate Condenser According to Kirchhoff;343
15.5;II.5. The Capacitance of a Leyden (Cylindrical Condenser);343
15.6;II.6. On the Definition of the Capacitance of Two Conductors with Equal and Opposite Charges;343
15.7;II.7. Characteristic Oscillations and Characteristic Frequencies of a Completely Conducting Cavity Bounded by a Rectangular Parallelepiped;345
15.8;II.8. Characteristic Oscillations and Characteristic Frequencies of the Interior of a Completely Conducting Circular Cylinder of Finite Length;345
15.9;II.9. Characteristic Oscillations within a Cavity Bounded by a Metal Sphere;345
15.10;II.10. Determination of the Propagation Constants of Wire Waves from Kelvin's Telegraph Equation and from Rayleigh's Alternating Current Resistance;345
16;PROBLEMS FOR PARTS III AND IV;345
16.1;III.1. The Lorentz Transformation for a Relative Motion Deviating from the x-Axis;345
16.2;III.2. On the Addition Theorem for Two Differently Directed Velocities;346
16.3;III.3. The Field of an Electron in Uniform Motion;346
16.4;III.4. On the Relativistic Energy Theorem for the Electron;346
16.5;III.5. The Electron in a Uniform Electrostatic Field;346
16.6;III.6. The Electron in a Uniform Magnetostatic Field;346
16.7;III.7. The Electron in a Uniform Electric Field and a Uniform Magnetic Field which is Parallel thereto;346
16.8;III.8. The Electron in a Uniform Electric Field and a Uniform Magnetic Field Perpendicular thereto;347
16.9;III.9. The Characteristic of the Thermionic Diode According to Langmuir and Schottky;347
16.10;III.10. The Acceleration of the Electron in the Betatron;348
16.11;IV.1. The Field of Unipolar Induction;348
17;ANSWERS AND COMMENTS;349
18;AUTHOR INDEX;380
19;SUBJECT INDEX;382