Electromagnetism

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Overview

Clearly developed from first principles, this introductory study supplies basic material on electrostatics and magnetostatics, then concentrates on electromagnetic theory — the authors are both leading men in the field. The book ranges freely over many areas of electromagnetic theory with some concern for electrical engineering. It covers the field theory of electromagnetism, electrostatics and the equations and theorems of Gauss, Poisson, Laplace and Green, solutions of Laplace's equation, dielectrics, magnetic fields of linear and circular currents, electromagnetic induction and Maxwell's equations, electromagnetic waves, electron theory, wave guides and cavity resonators, spherical electromagnetic waves, Huygen's principle and Green's theorem, and Fresnel and Fraunhofer diffraction. Practice problems are supplied at chapter ends.
Physicists and engineers will find this presentation particularly useful; but mathematicians have also used the book not only as an introduction to electromagnetism, but also as a means to an increased knowledge of the aims and tools of theoretical physics. The only background required to follow the development is a knowledge of the calculus and differential equations. More advanced mathematics is developed in appendixes.

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Product Details

  • ISBN-13: 9780486622637
  • Publisher: Dover Publications
  • Publication date: 2/17/2011
  • Series: Dover Books on Physics Series
  • Pages: 240
  • Sales rank: 984,234
  • Product dimensions: 5.40 (w) x 7.92 (h) x 0.49 (d)

Table of Contents

PREFACE
CHAPTER I THE FIELD THEORY OF ELECTROMAGNETISM
  Introduction
  1. The Force on a Charge
  2. The Field of a Distribution of Static Point Charges
  3. The Potentials
  4. Electric Images
    Problems
CHAPTER II ELECTROSTATICS
  Introduction
  1. Gauss's Theorem
  2. Capacity of Condensers
  3. Poisson's Equation and Laplace's Equation
  4. "Green's Theorem, and the Solution of Poisson's Equation in an Unbounded Region"
  5. Direct Solution of Poisson's Equation
    Problems
CHAPTER III SOLUTIONS OF LAPLACE'S EQUATION
  Introduction
  1. Solution of Laplace's Equation in Rectangular Coordinates by Separation of variables
  2. Laplace's Equation in Spherical Coordinates
  3. Spherical Harmonics
  4. Simple Solutions of Laplace's Equation in Spherical Coordinates
  5. The Dipole and the Double Layer
  6. Green's Solution for a Bounded Region
    Problems
CHAPTER IV DIELECTRICS
  Introduction
  1. The Polarization and the Displacement
  2. The Dielectric Constant
  3. Boundary Conditions at the Surface of a Dielectric
  4. "Electrostatic Problems Involving Dielectrics, and the Condenser"
  5. A Charge outside a Semi-infinite Dielectric Slab
  6. Dielectric Sphere in a Uniform Field
  7. Field in Flat and Needle-shaped Cavities
    Problems
CHAPTER V MAGNETIC FIELDS OF CURRENTS
  Introduction
  1. The Biot-Savart Law
  2. The Magnetic Field of a Linear and a Circular Current
  3. "The Divergence of B, and the Scalar Potential"
  4. The Magentic Dipole
  5. Ampère's Law
  6. The Vector Potential
    Problems
CHAPTER VI MAGNETIC MATERIALS
  Introduction
  1. The Magnetization Vector
  2. The Magnetic Field
  3. Magnetostatic Problems Involving Magnetic Media
  4. Uniformly Magnetized Sphere in an External Field
  5. Magnetomotive Force
    Problems
CHAPTER VII ELECTROMAGNETIC INDUCTION AND MAXWELL'S EQUATIONS
  Introduction
  1. The Law of Electromagnetic Induction
  2. Self- and Mutual Induction
  3. The Displacement Current
  4. Maxwell's Equations
  5. The Vector and Scalar Potentials
    Problems
CHAPTER VIII ELETROMAGNETIC WAVES AND ENERGY FLOW
  Introduction
  1. Plane Waves and Maxwell's Equations
  2. The Relation between E and H in a Plane Wave
  3. Electric and Magnetic Energy Density
  4. Poynting's Theorem and Poynting's Vector
  5. Power Flow and Sinusoidal Time Variation
  6. Power Flow and Energy Density in a Plane Wave
    Problems
CHAPTER IX ELECTRON THEORY AND DISPERSION
  Introduction
  1. Dispersion in Gases
  2. Dispersion in Liquids and Solids
  3. Dispersion in Metals
  4. The Quantum Theory and Dispersion
    Problems
CHAPTER X REFLECTION AND REFRACTION OF ELECTROMAGNETIC WAVES
  Introduction
  1. Boundary Conditions at a Surface of Discontinuity
  2. The Laws of Reflection and Refraction
  3. Reflection Coefficient at Normal Incidence
  4. Fresnel's Equation
  5. Total Reflection
  6. "Damped Plane Waves, Normal Incidence"
  7. "Damped Plane Waves, Oblique Incidence"
    Problems
CHAPTER XI WAVE GUIDES AND CAVITY RESONATORS
  Introduction
  1. Propagation between Two Parallel Mirrors
  2. Electromagnetic Field in the Wave Guide
  3. Examples of Wave Guides
  4. Standing Waves in Wave Guides
  5. Resonant Cavities
    Problems
CHAPTER XII SPHERICAL ELECTROMAGNETIC WAVES
  Introduction
  1. Maxwell's Equations in Spherical Coordinates
  2. Solutions of Maxwell's Equations in Spherical Coordinates
  3. The Field of an Oscillating Dipole
  4. The Field of a Dipole at Large Distances
  5. Scattering of Light
  6. Coherence and Incoherence of Light
    Problems
CHAPTER XIII HUYGENS' PRINCIPLE AND GREEN'S THEOREM
  Introduction
  1. The Retarded Potentials
  2. Mathematical Formulation of Huygens' Principle
  3. Integration for a Spherical Surface by Fresnel's Zones
  4. Huygens' Principle for Diffraction Problems
    Problems
CHAPTER XIV FRESNEL AND FRAUNHOFER DIFFRACTION
  Introduction
  1. Comparison of Fresnel and Fraunhofer Diffraction
  2. Fresnel Diffraction from a Slit
  3. Fraunhofer Diffraction from a Slit
  4. "The Circular Aperture, and the Resolving Power of a Lens"
  5. Diffraction from Several Slits; the Diffraction Grating
    Problems
APPENDIX I
  Vectors
    Vectors and Their Components
    Scalar and Vector Products of Two Vectors
    The Differentiation of Vectors
    The Divergence Theorem and Stoke's Theorem
    Problems
APPENDIX II
  Units
APPENDIX III
  Fourier Series
    Problems
APPENDIX IV
  Vector Operations in Curvilinear Coordinates
    Gradient
    Divergence
    Laplacian
    Curl
APPENDIX V
  Spherical Harmonics
APPENDIX VI
  Multipoles
APPENDIX VII
  Bessel's Functions
SUGGESTED REFERENCES
INDEX
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