Electromagnetism

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. Ampere'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