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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 | |