This is the first course in a two-semester sequence covering
classical electromagnetic theory at the graduate level. The
major topics for PHY 318 include electrostatics,
magnetostatics, electromagnetic induction, conservation laws,
an introduction to covariant electrodynamics, and
electromagnetic waves. The main purpose is teach students the
language and major concepts of electromagnetic theory in forms
that are useful for physics research as well as advanced
coursework in condensed matter physics, quantum field theory,
optical physics, and nuclear physics. The course may also be
useful to graduate students in other departments, for example,
chemistry and electrical engineering. PHY 318 includes a
substantial review electromagnetism at the intermediate
undergraduate level, through the assignment of several
intermediate level problems for homework.
Related courses and prerequisites:
The two courses most closely tied to PHY 318 are PHY 230 - a
prerequisite covering mathematical methods, and PHY 319 - the
second semester of the graduate electromagnetism sequence. The
PHY 230 material that is most useful for PHY 318 includes
ordinary differential equations, Sturm-Liouville theory,
techniques of complex variables (especially contour
integration), asymptotic expansions, and familiarity with
Mathematica. The continuation course PHY 319 focuses on the
following topics: an in-depth treatment of covariant
electrodynamics, radiation theory, waveguides, vector and
scalar diffraction theory, and special topics. A minimal
prerequisite for PHY 318/319 includes a good general physics
course in electricity and magnetism and knowledge of
mathematical techniques at the level of PHY 230; also, it is
strongly recommended that students should have taken at least
one semester of an intermediate undergraduate electromagnetism
course at the level of Griffiths.
Objectives:
To present the fundamental topics of classical electromagnetic
(EM) theory. A minimal set of topics includes: electrostatics
(including boundary value problems, variational methods,
method of images, Green function methods, multipole expansion,
Maxwell stress tensor, dielectric materials); magnetostatics;
magnetic materials; induction phenomena; Maxwell's equations;
gauge transformations; conservation theorems; EM field tensor;
transformation of E and B fields under Lorentz
transformation; EM waves in free space; scattering of EM waves
from planar dielectric interfaces; the Fresnel equations;
introduction to the general theory of frequency-dependent
dielectric functions. Much of the electrostatics discussion
centers around the development and use of mathematical
techniques for solving boundary value problems. The lectures
are generally at the level of Jackson, while the assigned
homework consists of a roughly equal mix of Jackson-level and
Griffiths-level problems.
Methods and Approach
Lectures:
PHY 318 is currently taught through 75-minute lectures (2 per
week) in which the instructor makes a chalkboard
presentation. Student are encouraged to ask questions.
Homework:
There are five required homework sets per semester. (There is
also one optional problem set at the very beginning of the
semester that reviews useful techniques of vector calculus.)
Each homework set consists of 10 - 12 problems, about half of
which are at the intermediate level - typically assigned from
Griffiths' text, while the remainder come from Jackson's text
or are developed by the instructor. The final problem set
typically includes 3 or 4 challenging problems that tie
together multiple concepts of the course. Students are
encouraged to discuss homework problems with their peers, the
instructor, and the TA. However, it is very important that
students write up their solutions independently.
Texts:
Currently, the two required texts are:
J. D. Jackson, Classical Electrodynamics,
3^{rd} ed.
D. J. Griffiths, Introduction to Electrodynamics,
3^{rd} ed.
Although the discussion in Jackson tends to be rather formal
and intricate, it remains the canonical graduate textbook for
classical electromagnetism. The problems are generally
challenging and a number of them help students develop both
their physical insight as well as their mathematical
abilities. Griffiths is an excellent intermediate-level
undergraduate text. With the possible exception of covariant
electrodynamics, the discussion is highly readable and
provides a good prelude to related material in Jackson.
Other texts that have been found to be useful for lecture
material and ideas for homework problems include:
Landau and Lifshitz, vol. 2, The Classical Theory of
Fields
Landau and Lifshitz, vol. 8, Electrodynamics of
Continuous Media
Francis E. Low, Classical Field Theory
Sandra C. Chapman, Core Electrodynamics
Exams and Grading:
There are two in-class 90 minute exams for this course. These
are closed book and closed notes exams, and consist of five
short answer questions and two problems. Exams are designed to
test students' factual knowledge of the material, ability to
formulate and solve problems, and ability to make
order-of-magnitude estimates. The first exam covers all of the
electrostatics material and is typically given in the seventh
week of the semester. The second exam covers all of the course
material up to electromagnetic waves and is typically given in
the 13^{th} week of the semester, approximately two
weeks prior to the last lecture of the course. The format and
difficulty of both exams is similar to the electromagnetism
part of the qualifying exam. In fact, one reason for giving
the second exam before semester's end is to ensure that
students receive effective feedback on their exam
performance. Grades are determined by the homework (40%), Exam
#1 (20 %), and Exam #2 (40%).
Sample Syllabus
318 sample lecturing schedule (assumes 75 minutes per
lecture).
L1 - Electrostatics: Coulomb's Law, electric field
L2 - Electrostatics: Gauss Law, potential, Laplace and
Poisson Equations
L3 - Electrostatics: conductors, uniqueness of solutions,
Green functions