Wilcox Contents1R

Macroscopic Electrodynamics I Physics 5330 Syllabus I. Survey and Introduction I.1 Charge conservation and quantization I.2 Quantum considerations I.3 Boundary conditions on fields I.4 Constitutive relations I.5 2-D constitutive relations Problems 1. Introduction to Electrostatics 1.1 Electric field definition 1.2 Dirac delta function properties 1.3 Gauss' law and solid angles 1.4 Deviations from inverse square law 1.5 Surface charge and dipole layers 1.6 Boundary conditions and uniqueness of solutions 1.7 Dirichlet and Neumann Green functions 1.8 Electrostatic energy 1.9 Capacitance Problems 2. Boundary Value Problems in Electrostatics 2.1 Method of images: flat conducting surface 2.2 Reduced Green function technique applied to flat conductor 2.3 Method of images: conducting sphere 2.4 Normal force on a charged surface 2.5 Charged conducting sphere force example 2.6 Expansion in orthogonal series: conducting box 2.7 Fourier series problems: conducting box 2.8 Separation of variables in cylindrical coordinates 2.9 Corner problem in cylindrical coordinates 2.10 Cylindrical halves at different potentials 2.11 Conformal mapping techniques Problems 3. Electrostatics: Cylidrical and Spherical Coordinates 3.1 Reduced Green function technique in cylindrical coordinates and Bessel functions 3.2 Orthogonality of Bessel functions 3.3 Zeros and completeness properties of Bessel functions 3.4 Reduced Green function for the conducting cylinder 3.5 The cylinder as a boundary value problem 3.6 Bessel functions of imaginary argument 3.7 Free charge solution using Bessel functions 3.8 Reduced Green function/image method: conducting wedge 3.9 Construction of spherical harmonics: Schwinger technique 3.10 Orthogonality properties of spherical harmonics 3.11 The Coulomb expansion, completeness of spherical harmonics and the "Addition Theorem" 3.12 Green function for concentric spheres 3.13 Conducting sphere in a uniform field 3.14 Method of last resort: eigenfunction expansions Problems 4. Multipoles, Electrostatics of Macroscopic Media, Dielectrics 4.1 Cartesian and spherical multipole expansions 4.2 Multipole energy expansions 4.3 External fields and forces on multipole distributions 4.4 Introduction of the "electric polarization" and "displacement field" 4.5 Green functions in the presence of linear dielectrics 4.6 Green function for the dielectric slab 4.7 Green function for the dielectric sphere 4.8 Field energy and dielectrics 4.9 Bulk forces on dielectrics: theory 4.10 Nonlinear dielectric example: a phenomenological quark confinement model 4.11 Bulk forces on dielectrics: examples Problems 5. Magnetostatics 5.1 Analogy to electrostatics 5.2 Equations of magnetostatics 5.3 Considerations leading to Ampere's law 5.4 Surface current considerations 5.5 Solid angle result for B 5.6 Circular current loop: solution using solid angle result for B 5.7 Circular current loop: direct solution 5.8 Current distributions and magnetic moments 5.9 External fields and forces on magnetic multipole distributions 5.10 Introduction of "magnetization" and the H field 5.11 Analogy with dielectrics 5.12 Image method for magnetostatics 5.13 Intrinsic and induced magnetization: theory and example Problems 6. Time Varying Fields I 6.1 Schwinger's plausibilty argument leading to Maxwell's equations 6.2 Faraday's law 6.3 Models introducing macroscopic Maxwell equations 6.4 Second-order formulation of Maxwell's equations 6.5 Energy and forces in magnetostatics 6.6 More on magnetostatic energies 6.7 Bulk forces on magnetic materials: theory and examples 6.8 Magnetic charge and the macroscopic Maxwell equations Problems