1 History and Perspective
  1.1 Brief History of the Science of Electromagnetism
  1.2 Electromagnetism in the Standard Model
 2 Vector Calculus
  2.1 Vector Algebra
   2.1.1 Definitions
   2.1.2 Addition and Multiplication of Vectors
   2.1.3 Vector Product Identities
   2.1.4 Geometric Meanings
  2.2 Vector Differential Operators
   2.2.1 Gradient of a Scalar Function
   2.2.2 Divergence of a Vector Function
   2.2.3 Curl of a Vector Function
   2.2.4 DelIdentities
  2.3 Integral Theorems
   2.3.1 Gauss's Theorem
   2.3.2 Stokes's Theorem
   2.3.3 Vector Calculus in Fluid Mechanics
  2.4 Curvilinear Coordinates
   2.4.1 General Derivations
   2.4.2 Cartesian, Cylindrical, and Spherical Coordinates
  2.5 The Helmholtz Theorem
 3 Basic Principles of Electrostatics
  3.1 Coulomb's Law
   3.1.1 The Superposition Principle
  3.2 The Electric Field
   3.2.1 Definition
   3.2.2 Charge as the Source of E
   3.2.3 Field of a Charge Continuum
  3.3 Curl and Divergence of E
   3.3.1 Field Theory Versus Action at a llistance
   3.3.2 Boundary Conditions of the Electrostatic rreia
  3.4 The Integral Form of Gauss's Law
  3.4.1Flux and Charge
   3.4.2 Proof of Gauss's Law
   3.4.3 Calculations Based on Gauss's Law
  3.5 Green's Function and the Dirac delta Function
   3.5.1 The Dirac delta Function
   3.5.2 Another Proof of Gauss's Law
  3.6 The Electric Potential
   3.6.1 Definition and Construction
   3.6.2 Poisson's Equation
   3.6.3 Example Calculations of V (x)
  3.7 Energy of the Electric Field
  3.8 The Multipole Expansion
   3.8.1 Two Charges
   3.8.2 The Electric Dipole
   3.8.3 Moments of a General Charge Distribution
   3.8.4 Equipotentials and Field Lines
   3.8.5 Torque and Potential Energy for a Dipole in an Electric Field
  3.9 Applications
  3.10 Chapter Summary
 4 Electrostatics and Conductors
  4.1 Electrostatic properties of conductors
  4.2 Electrostatic Problems with Rectangular Symmetry
   4.2.1 Charged Plates
   4.2.2 Problems with Rectangular Symmetry and External Point Charges. The Method of Images
  4.3 Problems with Spherical Symmetry
   4.3.1 Charged Spheres
   4.3.2 Problems with Spherical Symmetry and External Charges
  4.4 Problems with Cylindrical Symmetry
   4.4.1 Charged Lines and Cylinders
   4.4.2 Problems with Cylindrical Symmetry and an External Line Charge
 5 General Methods for Laplace's Equation
  5.1 Separation of Variables for Cartesian Coordinates
   5.1.1 Separable Solutions for Cartesian Coordinates j.r.t nxamptes
  5.2 Separation of Variables for Spherical Polar Coordinates
   5.2.1 Separable Solutions for Spherical Coordinates
   5.2.2 Legendre Polynomials
   5.2.3 Examples with Spherical Boundaries
  5.3 Separation of Variables for Cylindrical Coordinates
  5.3.1 Separable Solutions for Cylindrical Coordinates
  5.4 Conjugate Functions in 2 Dimensions
  5.5 Iterative Relaxation: A Numerical Method
 6 Electrostatics and Dielectrics
  6.1 The Atom as an Electric Dipole
   6.1.1 Induced Dipoles
   6.1.2 Polar Molecules
  6.2 Polarization and Bound Charge
  6.3 The Displacement Field
   6.3.1 Linear Dielectrics
   6.3.2 The Clausius-Mossotti Formula
   6.3.3 Poisson's Equation in a Uniform Linear Dielectric
  6.4 Dielectric Material in a Capacitor
   6.4.1 Design of Capacitors
   6.4.2 Microscopic Theory
   6.4.3 Energy in a Capacitor
   6.4.4 A Concrete Model of a Dielectric
  6.5 Boundary Value Problems with Dielectrics
   6.5.1 The Boundary Conditions
   6.5.2 A Dielectric Sphere in an Applied Field
   6.5.3 A Point Charge above a Dielectric with a Planar Bound-ary Surface
   6.5.4 A Capacitor Partially Filled with Dielectric
 7 Electric Currents
  7.1 Electric Current in a Wire
  7.2 Current Density and the Continuity Equation
   7.2.1 Local Conservation of Charge
   7.2.2 Boundary Condition on J(x, r)
  7.3 Current and Resistance
   7.3.1 Ohm's Law
   7.3.2 Fabrication of Resistors
   7.3.3 The Surface Charge en a Current Carrying Wire
  7.4 A Classical Model of Conductivity
  7.5 Joule's Law
  7.6 Decay of a Charge Density Fluctuation
  7.7 1-V Characteristic of a Vacuum-Tube Diode
  7.8 Chapter Summary
 8 Magnetostatics
  8.1 The Magnetic Force and the Magnetic Field
   8.1.1 Force on a Moving Charge
   8.1.2 Force on a Current-Carrying Wire
  8.2 Applications of the Magnetic Force
   8.2.1 Helical or Circular Motion of q in Uniform B
   8.2.2 Cycloidal Motion of q in Crossed E and B
   8.2.3 Electric Motors
  8.3 Electric Current as a Source of Magnetic Field
   8.3.1 The Biot-Savart Law
   8.3.2 Forces on Parallel Wires
   8.3.3 General Field Equations for B(x)
  8.4 Ampere's Law
   8.4.1 Ampere Law Calculations
   8.4.2 Formal Proof of Ampere's Law
  8.5 The Vector Potential 280
   8.5.1 General Solution for A(x)
  8.6 The Magnetic Dipole
   8.6.1 Asymptotic Analysis
   8.6.2 Dipole Moment of a Planar Loop
   8.6.3 Torque and Potential Energy of a Magnetic Dipole
   8.6.4 The Magnetic Field of the Earth
  8.7 The Full Field of a Current Loop
 9 Magnetic Fields and Matter
  9.1 The Atom as a Magnetic Dipole
   9.1.1 Diamagnetism
   9.1.2 Paramagnetism
  9.2 Magnetization and Bound Currents
   9.2.1 Examples
   9.2.2 A Geometric Derivation of the Bound Currents
  9.3 Am砂re's Law for Free Currents. and H
   9.3.1 The Integral Form of Ampere's Law
   9.3.2 The Constitutive Equation
   9.3.3 Magnetic Susceptibilities
   9.3.4 Boundary Conditions for Magnetic Fields
  9.4 Problems Involving Free Currents and Magnetic Materials
  9.5 A Magnetic Body in an External Field: The Magnetic Scalar Potential Φm(x)
  9.6 Ferromagnetism
   9.6.1 Measuring Magnetization Curves: The Rowland Ring
   9.6.2 Magnetization Curves of Ferromagnetic Materials
   9.6.3 The Permeability of a Ferromagnetic Material
 10 Electromagnetic Induction
  10.1 Motional EMF
   10.1.1 Electromotive Force
   10.1.2 EMF from Motion in B
   10.1.3 The Faraday Disk Generator
  10.2 Faraday's Law of Electromagnetic Induction
   10.2.1 Mathematical Statement
   10.2.2 Lenz's Law
   10.2.3 Eddy Currents
  10.3 Applications of Faraday's Law
   10.3.1 The Electric Generator and Induction Motor
   10.3.2 The Betatron
   10.3.3 Self-Inductance
   10.3.4 Classical Model of Diamagnetism
  10.4 Mutual Inductance
  10.5 Magnetic Field Energy
   10.5.1 Energy in a Ferromagnet
 11 The Maxwell Equations
  11.1 The Maxwell Equations in Vacuum and the Displacement Current
   11.1.1 The Displacement Current
  11.2 Scalar and Vector Potentials
   11.2.1 Gauge Transformations and Gauge Invariance
   11.2.2 Gauge Choices and Equations for A(x,t) and V(x,t)
  11.3 The Maxwell Equations in Matter
   11.3.1 Free and Bound Charge and Current
   11.3.2 Boundary Conditions of Fields
  11.4 Energy and Momentum of Electromagnetic Fields
   11.4.1 Poynting's Theorem
   11.4.2 Field Momentum
  11.5 Electromagnetic Waves in Vacuum
   11.5.1 Derivation of the Wave Equation
   11.5.2 An Example of a Plane Wave Solution
   11.5.3 Derivation of the General Plane Wave Solution
   11.5.4 A Spherical Harmonic Wave
   11.5.5 The Theory of Light
 12 Electromagnetism and Relativity
  12.1 Coordinate Transformations
   12.1.1 The Galilean Transformation
   12.1.2 The Lorentz Transformation
   12.1.3 Examples Involving the Lorentz Transformation
  12.2 Minkowski Space
   12.2.1 4-vectors, Scalars, and Tensors
   12.2.2 Kinematics of a Point Particle
   12.2.3 Relativistic Dynamics
  12.3 Electromagnetism in Covariant Form
   12.3.1 The Lorentz Force and the Field Tensor
   12.3.2 Maxwell's Equations in Covariant Form
   12.3.3 The 4-vector Potential
  12.4 Field Transformations
  12.5 Fields Due to a Point Charge in Uniform Motion
  12.6 Magnetism from Relativity
  12.7 The Energy-Momentum Flux Tensor
 13 Electromagnetism and Optics
  13.1 Electromagnetic Waves in a Dielectric
  13.2 Reflection and Refraction at a Dielectnc Interface
   13.2.1 Wave Vectors
   13.2.2 Reflectivity for Normal Incidence
   13.2.3 Reflection for Incidence at Arbitrary Angles: Fresnel's Equations
  13.3 Electromagnetic Waves in a Conductor
   13.3.1 Reflectivity of a Good Conductor
  13.4 A Classical Model of Dispersion: The Frequency Dependence of Material Properties
   13.4.1 Dispersion in a Dielectric
   13.4.2 Dispersion in a Plasma
 14 Wave Guides and Transmission Lines
  14.1 Electromagnetic Waves Between Parallel Conducting Planes
   14.1.1 The TEM Solution
   14.1.2 TE Waves
   14.1.3 TM Waves
   14.1.4 Summary
  14.2 The Rectangular Wave Guide 540
   14.2.1 Transverse Electric Modes TE(m, n)
   14.2.2 Transverse Magnetic Modes TM(m, n)
  14.3 Wave Guide of Arbitrary Shape 549
  14.4 The TEM Mode of a Coaxial Cable
  14.5 Cavity Resonance
 15 Radiation of Electromagnetic Waves
  15.1 The Retarded Potentials 561
   15.1.1 Green's Functions
  15.2 Radiation from an Electric Dipole
   15.2.1 The Hertzian Dipole
   15.2.2 Atomic Transitions
   15.2.3 Magnetic Dipole Radiation
   15.2.4 Complete Fields of a Hertzian Dipole
  15.3 The Half-Wave Linear Antenna
  15.4 The Larmor Formula: Radiation from a Point Charge
  15.5 Classical Electron Theory of Light Scattering
  15.6 Complete Fields of a Point Charge: The Li6nard-Wiechert Potentials
   15.6.1 A Charge with Constant Velocity
   15.6.2 The Complete Fields
   15.6.3 Generalization of the Larmor Formula
 A Electric and Magnetic Units
 B The Helmholtz Theorem
 Index