CAPSTONES IN PHYSICS:  Electromagnetism

Instructor:Prof. D. McIntyre, mcintyre@ucs.orst.edu

Office Weniger 463, available M 11-12, W 9-10, F 1-2 or by appointment

Text: Griffiths, Introduction to Electrodynamics, 3rd ed., Prentice-Hall, 1999. ISBN 0-13-805326-X

Supplementary: E. Purcell, Electricity and Magnetism (Berkeley Physics vol. 2)

Also recommended: Lorraine, Corson, and Lorraine, Electromagnetic Fields and Waves

Class Meetings: MWF 10:00-10:50, Weniger 275 

The capstone course in Electromagnetism aims to give an overview of the classical theory of electromagnetic fields and insight into its main applications.

Maxwell's Equations form the logical center of the course. They are the fountains from which all classical electromagnetism flows. These central equations are approached by examining their consequences in situations of increasing complication. The applications are arranged according to two organizing principles: complexity in time evolution, and in spatial geometry.

The simplest time dependence is obtained when all charges are stationary: electrostatics. Familiarity is assumed with examples in which the geometry is simplified by planar, cylindrical or spherical symmetry. The mathematical technique of asymptotic series expansions is seen to provide a universal treatment of the macroscopic effects of microscopic charge distributions at the atomic and molecular scale, via the electric dipole susceptibility. The boundaries between media are a subtle example of the microscopic vs. macroscopic duality.

The next-simplest time dependence occurs when charge flows steadily, providing time-independent currents: magnetostatics. The spatial treatment of magnetic fields echoes that of electrostatics, progressing from simple symmetric geometry, through a multipole expansion applied to microscopic currents, to the magnetic polarization and its behavior at boundaries. The existence of intrinsic dipoles, either elementary or compounded with atomic and nuclear motion, confronts the student with practically important examples of non-linear polarization.

Armed with an understanding of these cases, the full generality of Maxwell's equations is admired, and their conservation laws displayed. Their invariance with respect to translations in time, together with their linearity, permits Fourier decomposition of the solutions' time dependence, so that harmonic oscillations suffice as the most complicated time dependence to be considered in detail.

Harmonic solutions are first found in the absence of sources. As in the static cases, planar geometry provides the simplest example; a plane boundary introduces interesting complications of practical significance. Important examples of fancier geometry permit the understanding of waveguides, ubiquitous carriers of information.

Localized sources of radiation produce spherical waves, which are described in a multipole expansion analogous to the static cases. The mathematical treatment is simplified by the introduction of a magnetic vector potential, but its physical interpretation is problematic because of the gauge ambiguity. The first appearance of this nuisance gives little hint of its role as an overarching principle in quantum field theory!

Students' achievements will be evaluated based on four required activities:

1. Homework will be assigned weekly. A tentative list of homework assignments is published in the Syllabus. Solutions to assigned problems will be posted on the Web one week after they are assigned. Collaboration on homework exercises is encouraged provided proper attribution is given, but each student must write an independent presentation of the solution. To receive credit, work must be submitted before the solution is posted.

2. A Midterm Examination will be administered in class on October 27. Each student may consult a single sheet (8 1/2 x 11 inches, one side only) of notes written in the student's own hand, which must be submitted together with the student's answers.

3. A Project Report will be presented orally and visually on a topic assigned to the student by the instructor. Each student will be a member of a group which will prepare the visual presentation collaboratively. Topics and detailed project assignments will be given to the student in a conference with the instructor during the term.

4. A Final Examination will be administered on Thursday, December 11 at 6 pm. Each student may consult a single sheet (8 1/2 x 11 inches, both sides) of notes written in the student's own hand, which must be submitted together with the student's solutions.

The Inventory of Mastery lists 21 achievements expected of all students, and the homework assignments where you can expect to exhibit this mastery. The class examinations will focus on some of these items.

Graduate students registered for PH 531 will be assigned a more advanced project, and will be expected to demonstrate full mastery of a larger proportion of the required achievements, than undergraduates registered for PH 431.

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