Classical Theory of Electric and Magnetic Fields

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.

Contenu

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
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