Physics 5330: Syllabus

Classical Electrodynamics I
Physics 5330 Syllabus

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