Classical Theory of Electric and Magnetic Fields

Classical Theory of Electric and Magnetic Fields

1st Edition - January 1, 1971

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  • Authors: Roland H. Good, Terence J. Nelson
  • eBook ISBN: 9781483272030

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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


    I. Introduction

    Phenomena Governed by Maxwell'S Equations and the Lorentz Force

    Importance Of E & M in Understanding Modern Physics


    II. Development of Maxwell's Equations

    1. Electrostatics

    Review of Vector Notation

    Coulomb's Law


    Dipole Field

    The Continuity Equation

    Spherical Symmetry

    Electrostatic Potential


    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


    3. Faraday's Law of Induction

    4. Maxwell'S Displacement Current

    Final Form of Maxwell's Equations

    The Speed of Light



    III. Cartesian Vector and Tensor Analysis

    5. Notation

    Sum Convention

    Kronecker Delta Symbol

    The Levi-Civita Symbol


    6. Orthogonal Transformations

    Direction Cosines

    Transformation of Coordinates

    Rotations and Reflections


    7. Definition of Tensors

    Rank and Transformation Properties

    Importance of Tensors in Physics


    8. Co Variant Operations

    Covariance Distinguished from Invariance

    Examples of Covariant Operations




    9. Reduction of Tensors

    Simplification by Contraction and Symmetrization

    Irreducible Tensors



    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


    11. The General Electrostatic Boundary Value Problem

    Uniqueness of Solution

    Green's Function


    12. Solution by Images

    Conducting Planes

    Conducting Spheres

    Dirichlet Green's Function for a Sphere


    13. Inversion of Solutions

    Basic Theorem

    Geometry of Inversion

    Surface Charges

    Example of Inversion


    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


    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


    16. Dielectrics


    The Problem of a Condenser Filled with a Dielectric

    The Problem of a Charge near a Dielectric Boundary

    The Clausius-Mossotti Relation



    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


    18. Magnetization

    Concept of Bound Currents

    Field of a Uniformly Magnetized Sphere


    19. Multipole Expansion

    Expansion of the Vector Potential

    Expansion of the Scalar Potential

    Field of a Magnetized Object


    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


    22. Mechanical Properties of the Field



    Angular Momentum

    Thermodynamics of Field and Material

    Electrostatic Energy in Terms of Sources

    Magnetostatic Energy in Terms of Sources


    Magnetostatic Assembly Work


    23. Potentials

    The Vector and Scalar Potentials

    Lorentz Gauge

    Hertz Potential

    Coulomb Gauge


    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)


    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



    VIII. The Special Theory of Relativity

    26. Before Einstein

    27. Einstein's Theory

    The Principle of Special Relativity

    Properties of Lorentz Transformations


    28. Relativistic Mechanics of Point Particles

    Proper Time

    Energy and Momentum in Relativistic Mechanics



    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


    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



    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


    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


    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


    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




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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