1. Introduction and Perspectives

• 1.1 Maxwell’s equations
• 1.2 Relativistic and quantum considerations
• 1.3 Macroscopic Maxwell’s equations
• 1.4 Boundary conditions on field
• 1.5 Two-dimensional electrodynamics and boundary conditions
  Exercises

2. Introduction to Electrostatics

• 2.1 Electric field:definition
• 2.2 The Dirac delta function and singular charge distributions
• 2.3 Line and surface delta functions
• 2.4 Gauss’ law and solid angles
• 2.5 Verification of the inverse square law: the Cavendish experiment
• 2.6 Surface charge and dipole layers
• 2.7 Boundary conditions and uniqueness of solutions
• 2.8 Dirichlet and Neumann Green functions
• 2.9 One-dimensional Green function examples
• 2.10 Electrostatic energy
• 2.11 Normal force on a charged surface
• 2.12 Capacitance
  Exercises

3. Boundary Value Problem in Electrostatics

• 3.1 Conducting plane: Green functions and method of images
• 3.2 Reduced Green function technique applied to flat conductor
• 3.3 Method of images: conducting sphere
• 3.4 Charged conducting sphere force example
• 3.5 Separation of variables: conducting box
• 3.6 Eigenfunction expansion of Green function for a conducting box
• 3.7 Separation of variables in polar coordinates
• 3.8 Corner problems in polar coordinates
• 3.9 Cylindrical halves at different potentials
• 3.10 Variational methods
• 3.11 Conformal mapping techniques
  Exercises

4. Electrostatics in Cylindrical and Spherical Coordinates

• 4.1 Cylindrical coordinates and Bessel functions/li>
• 4.2 Completeness of Bessel functions
• 4.3 Zeros and orthogonality properties of Bessel functions
• 4.4 Reduced Green function for the conducting cylinder
• 4.5 Potential inside a cylinder as a boundary value problem
• 4.6 Bessel functions of imaginary argument; asymptotic forms of Bessel functions
• 4.7 Cylindrical free-space Green function using the Wronskian technique
• 4.8 Reduced Green function method for the conducting wedge and image interpretation
• 4.9 Schwinger’s construction of spherical harmonics
• 4.10 Orthogonality properties of spherical harmonics
• 4.11 The Coulomb expansion, completeness of spherical harmonics and the “Addition Theorem”
• 4.12 Green function for concentric spheres
• 4.13 Potential of conducting sphere in a uniform field via separation of variables
• 4.14 Method of last resort: eigenfunction expansions
  Exercises

5. Multipoles, Electrostatics of Macroscopic Media, Dielectrics

• 5.1 Cartesian and spherical multipole expansions
• 5.2 Multipole energy expansions
• 5.3 External fields and forces on multipole distributions
• 5.4 Electric polarization and the displacement field
• 5.5 Green functions in the presence of linear dielectrics
• 5.6 Green function for the dielectric slab
• 5.7 Green function for the dielectric sphere
• 5.8 Field energy and dielectrics
• 5.9 Bulk forces on dielectrics: theory
• 5.10 Nonlinear dielectric example: leading logarithm
  model
• 5.11 Bulk forces on dielectrics: examples
  Exercises

6. Magnetostatics

• 6.1 Analogy to electrostatics
• 6.2 General equations for magnetostatics
• 6.3 Ampere’s law; vector potentials
• 6.4 Surface current considerations
• 6.5 Solid angle result for B
• 6.6 Circular current loop: solution using solid angle result for B
• 6.7 Circular current loop: direct solution
• 6.8 Current distributions and magnetic moments
• 6.9 External fields and forces on magnetic multipole distributions
• 6.10 Introduction of “magnetization” and the H field
• 6.11 Boundary conditions at material interfaces
• 6.12 Image method for magnetostatics
• 6.13 Intrinsic and induced magnetization: theory and example
  Exercises

7. Time Varying Fields I

• 7.1 Plausibility argument leading to Maxwell’s equations
• 7.2 Faraday’s law
• 7.3 Derivations of macroscopic Maxwell equations
• 7.4 Second-order formulation of the vacuum Maxwell equations
• 7.5 Magnetostatic field energy
• 7.6 Magnetostatic field energy and forces on current loops
• 7.7 Bulk forces on magnetic materials: theory and examples
• 7.8 Magnetic charge and the macroscopic Maxwell equations
  Exercises