# Electrodynamics

## 1st Edition

### Lectures on Theoretical Physics, Vol. 3

**Author:**Arnold Sommerfeld

**eBook ISBN:**9781483214290

**Imprint:**Academic Press

**Published Date:**1st January 1964

**Page Count:**386

## Description

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.

## Table of Contents

Preface v

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

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 εο, μo 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 Equations

9. The Simplest Boundary-Value Problems of Electrostatics

A. Charging Problems

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 Semiinfinite 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. Specific 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. Thermodynamics

15. Stationary Currents and Their Magnetic Field. Method of the Vector Potential

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. Self inductance of the Two-Wire Line

F. General Theorem Regarding Energy Transmission by Stationary Currents

16. Ampére's Method of the Magnetic Double Layer

A. The Magnetic Shell for Linear Conductors

B. Magnetic Energy and Magnetic Flux

C. Application to the Self inductance 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

B. The Wheatstone Bridge

C. Coupled Circuits

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 Symmetry. Details on Alternating Current Impedance and Skin Effect

A. Longitudinal and Transverse 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 Cylindrical 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 Hv = Ηφ

E. The Boundary Condition for Ex 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 2

B. The Magnetic Analog to the Lorentz Force

C. The Intrinsic Field of an Electron in Uniform 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 Ω

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 between Momentum and Energy

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's Theory for Moving Bodies 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 Electron by Radiation and Its Reaction on the Motion

37. Approaches to the Generalization of Maxwell's Equations and to the Theory of the Elementary Particles

38. General Theory of Relativity; Unified Theory of Gravitation and Electrodynamics

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

I.3. The Magnetic Excitation within an Infinitely Long Solenoid

I.4. The Cosine Law of Spherical Trigonometry as Special Case of a General 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 Comparison 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 Capacitance 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 Completely Conducting Cavity Bounded by a Rectangular Parallelepiped

II.8. Characteristic Oscillations and Characteristic Frequencies of the Interior 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 Electron in the Betatron

IV.l. The Field of Unipolar Induction

Answers and Comments

Author Index

Subject Index

## Details

- No. of pages:
- 386

- Language:
- English

- Copyright:
- © Academic Press 1952

- Published:
- 1st January 1964

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483214290

## About the Author

### Arnold Sommerfeld

### Affiliations and Expertise

University of Munich