P506 Electricity and Magnetism

Class meets TR 1:25-3:20 in SW 217

Chuck Horowitz

Office: SW 233, phone 5-0303

Email: horowit@indiana.edu

Text: “Electrodynamics” by J. D. Jackson

Grading is based on homework (40%), a midterm (25%), and a final (35%).  The homework (about one assignment per week) is the heart of the class and very important.

Grader: Ruizi Li, email: ruizli@indiana.edu,  SW340, 5-0293

Course description:

(4 cr.) Electricity and Magnetism I Three hours of lectures and one hour of recitation. Development of Maxwell's equations. Conservation laws. Problems in electrostatics and magnetostatics. Introduction to the special functions of mathematical physics. Time-dependent solutions of Maxwell's equations. Motion of particles in given electromagnetic fields. Elementary theory of radiation. Plane waves in dielectric and conducting media. Dipole and quadruple radiation from nonrelativistic systems.

Outline:

I) Introduction to electrostatics.

II) Boundary value problems in electrostatics.

III) Multipoles, electrostatics of macroscopic media.

IV) Magnetostatics, Faraday’s law.

V) Maxwell equations, conservation laws.

VI) Plane electromagnetic waves and wave propagation (start).

The course will cover approximately the first 6 chapters of Jackson.

Mathematical Methods in the Core Graduate Courses

Physics P506 (Electricity and Magnetism I)

1. Calculus: Cylindrical, spherical, coordinate systems, transformations of basis vectors, Jacobians, differential operators in orthogonal curvilinear coordinates.
2. Delta Functions: Symbolic rules, properties, changes of variable, redundant coordinates.
3. Green's Functions: Gauss and Stokes Theorems, Green's Theorems, Green's functions for the Laplacean on Rn, n=1,2,3 directly and by Fourier transform, Green's functions on bounded regions for Dirichlet and Neumann problems.
4. Separation of variables for the Laplace operator: (a) Two dimensional boundary value problems and Fourier series, Fourier series expansions for Green's functions. (b) Spherical coordinates, Gamma Function, Legendre polynomials and expansions, orthogonality relations, associated Legendre functions, orthogonality relations, spherical harmonics, orthogonality relations, addition theorem for spherical harmonics, spherical harmonic expansions for Green's functions. (c) Cylindrical coordinates, Bessel functions (J in some detail as a power series solution to the ordinary differential equation, regular singular points, other Bessel functions and their asymptotic properties near the origin and at infinity), Fourier-Bessel series, Wronskians for second order ordinary differential equations, Fourier-Bessel expansions of Green's functions.
5. Numerical Methods: Iterative solutions to Laplace's equation, comparison between analytical and numerical results, treatment of problems with less symmetry than the usual analytical exercises.