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History and Perspective | |

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Brief History of the Science of Electromagnetism | |

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Electromagnetism in the Standard Model | |

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Vector Calculus | |

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Vector Algebra | |

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Definitions | |

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Addition and Multiplication of Vectors | |

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Vector Product Identities | |

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Geometric Meanings | |

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Vector Differential Operators | |

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Gradient of a Scalar Function | |

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Divergence of a Vector Function | |

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Curl of a Vector Function | |

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Del Identities | |

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Integral Theorems | |

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Gauss's Theorem | |

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Stokes's Theorem | |

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Vector Calculus in Fluid Mechanics | |

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Curvilinear Coordinates | |

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General Derivations | |

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Cartesian, Cylindrical, and Spherical Coordinates | |

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The Helmholtz Theorem | |

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Basic Principles of Electrostatics | |

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Coulomb's Law | |

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The Superposition Principle | |

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The Electric Field | |

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Definition | |

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Charge as the Source of E | |

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Field of a Charge Continuum | |

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Curl and Divergence of E | |

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Field Theory Versus Action at a Distance | |

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Boundary Conditions of the Electrostatic Field | |

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The Integral Form of Gauss's Law | |

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Flux and Charge | |

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Proof of Gauss's Law | |

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Calculations Based on Gauss's Law | |

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Green's Function and the Dirac delta Function | |

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The Dirac delta Function | |

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Another Proof of Gauss's Law | |

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The Electric Potential | |

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Definition and Construction | |

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Poisson's Equation | |

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Example Calculations of V (x) | |

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Energy of the Electric Field | |

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The Multipole Expansion | |

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Two Charges | |

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The Electric Dipole | |

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Moments of a General Charge Distribution | |

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Equipotentials and Field Lines | |

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Torque and Potential Energy for a Dipole in an Electric Field | |

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Applications | |

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Chapter Summary | |

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Electrostatics and Conductors | |

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Electrostatic properties of conductors | |

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Electrostatic Problems with Rectangular Symmetry | |

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Charged Plates | |

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Problems with Rectangular Symmetry and External Point Charges. The Method of Images | |

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Problems with Spherical Symmetry | |

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Charged Spheres | |

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Problems with Spherical Symmetry and External Charges | |

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Problems with Cylindrical Symmetry | |

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Charged Lines and Cylinders | |

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Problems with Cylindrical Symmetry and an External Line Charge | |

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General Methods for Laplace's Equation | |

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Separation of Variables for Cartesian Coordinates | |

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Separable Solutions for Cartesian Coordinates | |

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Examples | |

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Separation of Variables for Spherical Polar Coordinates | |

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Separable Solutions for Spherical Coordinates | |

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Legendre Polynomials | |

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Examples with Spherical Boundaries | |

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Separation of Variables for Cylindrical Coordinates | |

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Separable Solutions for Cylindrical Coordinates | |

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Conjugate Functions in 2 Dimensions | |

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Iterative Relaxation: A Numerical Method | |

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Electrostatics and Dielectrics | |

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The Atom as an Electric Dipole | |

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Induced Dipoles | |

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Polar Molecules | |

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Polarization and Bound Charge | |

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The Displacement Field | |

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Linear Dielectrics | |

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The Clausius-Mossotti Formula | |

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Poisson's Equation in a Uniform Linear Dielectric | |

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Dielectric Material in a Capacitor | |

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Design of Capacitors | |

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Microscopic Theory | |

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Energy in a Capacitor | |

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A Concrete Model of a Dielectric | |

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Boundary Value Problems with Dielectric | |

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The Boundary Conditions | |

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A Dielectric Sphere in an Applied Field | |

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A Point Charge above a Dielectric with a Plannar Boundary Surface | |

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A Capacitor Partially Filled with Dielectric | |

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Electric Currents | |

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Electric Current in a Wire | |

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Current Density and the Continuity Equation | |

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Local Conservation of Charge | |

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Boundary Condition on J(x, t) | |

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Current and Resistance | |

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Ohm's Law | |

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Fabrication of Resistors | |

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The Surface Charge on a Current Carrying Wire | |

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A Classical Model of Conductivity | |

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Joule's Law | |

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Decay of a Charge Density Fluctuation | |

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I-V Characteristic of a Vacuum-Tube Diode | |

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Chapter Summary | |

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Magnetostatics | |

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The Magnetic Force and the Magnetic Field | |

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Force on a Moving Charge | |

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Force on a Current-Carrying Wire | |

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Applications of the Magnetic Force | |

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Helical or Circular Motion of q in Uniform B | |

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Cycloidal Motion of q in Crossed E and B | |

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Electric Motors | |

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Electric Current as a Source of Magnetic Field | |

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The Biot-Savart Law | |

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Forces on Parallel Wires | |

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General Field Equations for B(x) | |

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Ampere's Law | |

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Ampere Law Calculations | |

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Formal Proof of Ampere's Law | |

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The Vector Potential | |

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General Solution for A(x) | |

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The Magnetic Dipole | |

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Asymptotic Analysis | |

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Dipole Moment of a Planar Loop | |

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Torque and Potential Energy of a Magnetic Dipole | |

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The Magnetic Field of the Earth | |

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The Full Field of a Current Loop | |

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Magnetic Fields and Matter | |

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The Atom as a Magnetic Dipole | |

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Diamagnetism | |

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Paramagnetism | |

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Magnetization and Bound Currents | |

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Examples | |

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A Geometric Derivation of the Bound Currents | |

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Ampere's Law for Free Currents, and H | |

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The Integral Form of Ampere's Law | |

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The Constitutive Equation | |

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Magnetic Susceptibilities | |

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Boundary Conditions for Magnetic Fields | |

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Problems Involving Free Currents and Magnetic Materials | |

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A Magnetic Body in an External Field: The Magnetic Scalar Potential [phi subscript m](x) | |

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Ferromagnetism | |

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Measuring Magnetization Curves: The Rowland Ring | |

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Magnetization Curves of Ferromagnetic Materials | |

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The Permeability of a Ferromagnetic Material | |

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Electromagnetic Induction | |

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Motional EMF | |

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Electromotive Force | |

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EMF from Motion in B | |

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The Faraday Disk Generator | |

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Faraday's Law of Electromagnetic Induction | |

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Mathematical Statement | |

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Lenz's Law | |

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Eddy Currents | |

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Applications of Faraday's Law | |

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The Electric Generator and Induction Motor | |

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The Betatron | |

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Self-Inductance | |

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Classical Model of Diamagnetism | |

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Mutual Inductance | |

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Magnetic Field Energy | |

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Energy in a Ferromagnet | |

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The Maxwell Equations | |

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The Maxwell Equations in Vacuum and the Displacement Current | |

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The Displacement Current | |

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Scalar and Vector Potentials | |

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Gauge Transformations and Gauge Invariance | |

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Gauge Choices and Equations for A(x,t) and V(x,t) | |

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The Maxwell Equations in Matter | |

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Free and Bound Charge and Current | |

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Boundary Conditions of Fields | |

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Energy and Momentum of Electromagnetic Fields | |

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Poynting's Theorem | |

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Field Momentum | |

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Electromagnetic Waves in Vacuum | |

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Derivation of the Wave Equation | |

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An Example of a Plane Wave Solution | |

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Derivation of the General Plane Wave Solution | |

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A Spherical Harmonic Wave | |

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The Theory of Light | |

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Electromagnetism and Relativity | |

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Coordinate Transformations | |

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The Galilean Transformation | |

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The Lorentz Transformation | |

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Examples Involving the Lorentz Transformation | |

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Minkowski Space | |

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4-vectors, Scalars, and Tensors | |

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Kinematics of a Point Particle | |

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Relativistic Dynamics | |

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Electromagnetism in Covariant Form | |

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The Lorentz Force and the Field Tensor | |

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Maxwell's Equations in Covariant Form | |

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The 4-vector Potential | |

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Field Transformations | |

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Fields Due to a Point Charge in Uniform Motion | |

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Magnetism from Relativity | |

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The Energy-Momentum Flux Tensor | |

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Electromagnetism and Optics | |

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Electromagnetic Waves in a Dielectric | |

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Reflection and Refraction at a Dielectric Interface | |

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Wave Vectors | |

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Reflectivity for Normal Incidence | |

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Reflection for Incidence at Arbitrary Angles: Fresnel's Equations | |

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Electromagnetic Waves in a Conductor | |

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Reflectivity of a Good Conductor | |

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A Classical Model of Dispersion: The Frequency Dependence of Material Properties | |

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Dispersion in a Dielectric | |

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Dispersion in a Plasma | |

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Wave Guides and Transmission Lines | |

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Electromagnetic Waves Between Parallel Conducting Planes | |

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The TEM Solution | |

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TE Waves | |

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TM Waves | |

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Summary | |

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The Rectangular Wave Guide | |

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Transverse Electric Modes TE(m, n) | |

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Transverse Magnetic Modes TM(m, n) | |

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Wave Guide of Arbitrary Shape | |

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The TEM Mode of a Coaxial Cable | |

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Cavity Resonance | |

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Radiation of Electromagnetic Waves | |

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The Retarded Potentials | |

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Green's Functions | |

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Radiation from an Electric Dipole | |

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The Hertzian Dipole | |

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Atomic Transitions | |

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Magnetic Dipole Radiation | |

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Complete Fields of a Hertzian Dipole | |

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The Half-Wave Linear Antenna | |

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The Larmor Formula: Radiation from a Point Charge | |

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Classical Electron Theory of Light Scattering | |

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Complete Fields of a Point Charge: The Lienard-Wiechert Potentials | |

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A Charge with Constant Velocity | |

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The Complete Fields | |

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Generalization of the Larmor Formula | |

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Electric and Magnetic Units | |

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The Helmholtz Theorem | |

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Index | |