# Classical Theory of Electric and Magnetic Fields

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Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains magnetostatics and compares the calculation methods of electrostatics with those of magnetostatics. The book also discusses electromagnetic wave phenomena concerning wave equations with a source term and the Maxwell equations which are linear and homogenous. The book also explains Einstein's the Special Theory of Relativity which is applicable' only to inertial coordinate systems. The text also discusses the particle aspects of electromagnetic field equations such as those concerning wave equations for particles with spin. This textbook is intended for graduate or advanced students and academicians in the field of physics.

## Table of Contents

Preface

Acknowledgments

I. Introduction

Phenomena Governed by Maxwell'S Equations and the Lorentz Force

Importance Of E & M in Understanding Modern Physics

References

II. Development of Maxwell's Equations

1. Electrostatics

Review of Vector Notation

Coulomb's Law

Distributions

Dipole Field

The Continuity Equation

Spherical Symmetry

Electrostatic Potential

Problems

2. Magnetostatics

Ampere's Law

Magnetic Field of a Long Straight Wire

Curl and Divergence of the Magnetic Field

The Case When the Curl Vanishes

Determination of a Field by Its Divergence and Curl

The Vector Potential

Cylindrical Symmetry

Problems

3. Faraday's Law of Induction

4. Maxwell'S Displacement Current

Final Form of Maxwell's Equations

The Speed of Light

Problem

References

III. Cartesian Vector and Tensor Analysis

5. Notation

Sum Convention

Kronecker Delta Symbol

The Levi-Civita Symbol

Problems

6. Orthogonal Transformations

Direction Cosines

Transformation of Coordinates

Rotations and Reflections

Problem

7. Definition of Tensors

Rank and Transformation Properties

Importance of Tensors in Physics

Problems

8. Co Variant Operations

Covariance Distinguished from Invariance

Examples of Covariant Operations

Pseudotensors

Differentiation

Problems

9. Reduction of Tensors

Simplification by Contraction and Symmetrization

Irreducible Tensors

Problem

Reference

IV. Electrostatics

10. Fields near Singular Sources

Expansion of Potential Outside Charges

The Quadrupole Moment Tensor

Energy of Singular Sources in an External Electrostatic Field

Surface Singularities

Problems

11. The General Electrostatic Boundary Value Problem

Uniqueness of Solution

Green's Function

Problems

12. Solution by Images

Conducting Planes

Conducting Spheres

Dirichlet Green's Function for a Sphere

Problems

13. Inversion of Solutions

Basic Theorem

Geometry of Inversion

Surface Charges

Example of Inversion

Problems

14. Solution by Complex Variable Technique

Differentiation of a Function of a Complex Variable

Integration on Closed Paths in the Complex Plane

Analytic Functions as Solutions of Laplace's Equation

Application to Electrostatics

Problems

15. Method of Separation of Variables

Separation of Laplace's Equation in Spherical Coordinates

Summary of Properties of the Spherical Harmonics

Multipole Expansion of the Potential of a Distribution of Charges

The Quadrupole Moment in Nuclear Physics

Separation of Laplace's Equation in Cylindrical Coordinates

Expansions in Complete Sets of Functions

Eigenfunction Expansion of the Dirichlet Green's Function

Problems

16. Dielectrics

Polarization

The Problem of a Condenser Filled with a Dielectric

The Problem of a Charge near a Dielectric Boundary

The Clausius-Mossotti Relation

Problems

References

V. Magnetos tatics

17. The Magnetic Dipole

Field of a Magnetic Dipole

Force on a Dipole in an External Field

Singularities in the Dipole Field

The Gyromagnetic Ratio

Problem

18. Magnetization

Concept of Bound Currents

Field of a Uniformly Magnetized Sphere

Problems

19. Multipole Expansion

Expansion of the Vector Potential

Expansion of the Scalar Potential

Field of a Magnetized Object

Problems

VI. Dynamical Maxwell Equations

20. Final Form of Maxwell's Equations

21. Units and Dimensions

Gaussian Units

Heaviside-Lorentz Units

Electrostatic Units

Electromagnetic Units

MKS (Meter-Kilogram-Second) Units

Problem

22. Mechanical Properties of the Field

Momentum

Energy

Angular Momentum

Thermodynamics of Field and Material

Electrostatic Energy in Terms of Sources

Magnetostatic Energy in Terms of Sources

Inductance

Magnetostatic Assembly Work

Problems

23. Potentials

The Vector and Scalar Potentials

Lorentz Gauge

Hertz Potential

Coulomb Gauge

Problem

VII. Wave Phenomena

24. The Wave Equation

Special Cases

Initial Value Problem in One Dimension

Source Problem in One Dimension

Initial Value Problem in Three Dimensions

Source Problem in Three Dimensions (Green's Function Solution)

Problems

25. Plane Waves

Plane Waves in Linear Insulators

Reflection and Refraction at a Dielectric Interface

Phase and Group Velocity

Classical Model of a Dielectric with Dispersion, Resonance, and Absorption

Causality and Dispersion Relations

Problems

References

VIII. The Special Theory of Relativity

26. Before Einstein

27. Einstein's Theory

The Principle of Special Relativity

Properties of Lorentz Transformations

Problem

28. Relativistic Mechanics of Point Particles

Proper Time

Energy and Momentum in Relativistic Mechanics

Forces

Problems

29. Covariance of E & M

The Four-Dimensional Form of Maxwell1 s Equations

Lorentz Tensors with Zero Divergence

Stress-Energy-Momentum Tensor

Aberration and the Doppler Effect

Problems

30. Motion of a Particle with a Intrinsic Magnetic Moment

Intrinsic Properties of Elementary Particles

Lorentz Transformation from the Rest System to the Lab

Covariant Description of the Particle's Motion and Orientation

Generalization of the Equations of Motion from the Rest to the Lab Frame

Problems

References

IX. Radiation

31. The Long Wavelength Approximation

Distinction between the Near Field and the Far Field

Expansion far from Sources

Electric Dipole Radiation

Magnetic Dipole Radiation

Electric Quadrupole Radiation

Problems

32. Radiation from Source Distributions Comparable to a Wavelength in Extent

Radiation from a Center-Fed Linear Antenna

Electric and Magnetic Fields of a Moving Point Charge

Radiation from an Accelerated Charge

Spectral Distribution of Radiation from a Moving Charge

Cerenkov Radiation 534; Problems

References

X. Waves and Metallic Boundary Conditions

33. Waveguides and Resonant Cavities

Wave Propagation in Good Conductors

Zero-Order Surface Effects

First-Order Surface Effects

Propagation between Two Mirrors

General Theory for Propagation in a Guide of Uniform Cross Section

Modes in a Rectangular Guide

The Rectangular Resonant Cavity with Only TE10 above Cutoff

Problem

XI. Particle Aspects of Electromagnetic Field Equations

34. Introduction to Wave Equations for Particles with Spin

Particle States and Fields

Plane Wave Solutions

35. Particle Aspects of Electromagnetic Field Equations

Hamiltonian and Wave Function for the Photon

Transformation Properties of the Wave Function

Covariantly Defined Matrices

Manifestly Covariant Wave Equations

Invariant Inner Product

Energy, Momentum, and Angular Momentum Operators

Uncertainty Principle for Photons

Problems

References

Index

## Product details

- No. of pages: 654
- Language: English
- Copyright: © Academic Press 1971
- Published: January 1, 1971
- Imprint: Academic Press
- eBook ISBN: 9781483272030

## About the Authors

### Roland H. Good

### Terence J. Nelson

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