Physics 210A, Winter 2008, Electromagnetic Theory

Mon, Wed 11am-12:15pm Girvetz Room 2129

Douglas M. Eardley
<doug@kitp.ucsb.edu> (the best way to reach me)
Phone: -2280, Fax: -2431 Office hours this week are 2:30-4pm Fridays, Room 2329 KITP (Kohn Hall). If you want to meet me at another time, email or call first to make an appointment.

TA: Hieu Nguyen <doubleslash@gmail.com>, office hours Mon and Thu, 12-1:30pm.

Course Web Page (this page):

http://online.kitp.ucsb.edu/~doug/phys210/
http://www.kitp.ucsb.edu/~doug/phys210/      mirror site

It will be updated steadily as the course goes on, so please visit it frequently.

1.  Subject

This class is the first quarter of a 2-quarter introductory course on classical electrodynamics at the graduate level.  The entire course will cover these important topics: Electrostatics, magnetostatics, boundary value problems, time varying fields, Maxwell's equations, radiation, multipole fields, scattering, and relativistic particle dynamics.

2. Book

The required text for the entire course is Classical Electrodynamics (3rd Ed, 1998), by John David Jackson (John Wiley & Sons; ISBN: 0-471-30932-X), available through (e.g.) www.amazon.com, www.wiley.com, or in the UCSB bookstore. We will cover the first half of the book winter quarter.

3. Syllabus for 210A Winter Quarter

WeekTopicChapter
Jan 7Introduction to E&MSurvey,1
Jan 14Electrostatics1
Jan 21Boundary value problems2
Jan 28Boundary value problems3
Feb 4Dielectrics4
Feb 11Midterm exam; Magnetism5
Feb 18Magnetic materials5
Feb 25Maxwell equations & conservation laws6
Mar 3Electromagnetic waves7
Mar 10Wave propagation7,8
Mar 17Final exam

Dates may vary, please check this webpage often for the latest information.

4. Schedule for Winter Quarter (subject to slight adjustments)

5. Coursework and grading

Course grading will be tentatively 60% homework, 30% final, 10% midterm. The midterm and final exams will be open-book, take-home exams.

Homework will be due Tuesdays in TA Hieu Nguyen's mailbox in Room 5340 Broida Hall (the palatial Graduate Lounge), by 4:30pm. Homework 1 will be due Tuesday, Jan 15. Late homework will be accepted only at the convenience of the TA; please get approval beforehand from the TA or professor. Solutions will be posted later.


Week of January 7

Reading: Jackson Chapter I (Introduction and Survey); begin Chapter 1 (Electrostatics).

No class Wednesday Jan 9.

No Homework this week.


Week of January 14

Reading: Jackson Chapter 1 (Electrostatics).

Homework set 1: Due Tuesday Jan 15. Jackson Chapter 1, pages 50ff, problems 1.1, 1.5. Solutions 1 are available here.


Week of January 21

Mon Jan 21 is a University holiday; no class.

Reading: Begin Chapter 2 on boundary-value problems.

Homework set 2: Due Tuesday Jan 22. Jackson Chapter 1, pages 50ff, problems 1.6+, 1.8+, 1.10, 1.13*, 1.19**. Solutions 2 are available here.
Explanations:
+In problems 1.6 & 1.8, you may use the standard formulas for a capacitor: Q=CV, W=Q2/2C = CV2/2.
*Problems 1.13 & 1.19 depend on previous problems, namely 1.12 and 1.17. You need not do 1.12 or 1.17 (though you may find them interesting).
**In problem 1.19, there is a clash of notation: ρ (greek "rho") is just the radial coordinate here, in the cylindrical coordinate system. The charge density ρ does not appear at all in this problem.


Week of January 28

Reading: Chapter 2; begin Chapter 3 (on boundary value problems).

Homework set 3: Due Tuesday Jan 29. Jackson Chapter 2, pages 85ff, problems 2.1, 2.4, 2.7, 2.9, 2.15. Solutions 3 are available here.


Week of February 4

Reading: Chapter 3 (Boundary Value Problems in Electrostatics II). Begin Chapter 4 (Multipoles...)

Homework set 4: Due Tuesday Feb 5. Jackson Chapter 2, pages 85ff, problems 2.23, 2.26ab (omit c); and Chapter 3, pp135ff, problems 3.1, 3.6, 3.9. Solutions 4 are available here.


Week of February 11

Reading: Chapter 4 (Multipoles...). Begin Chapter 5.

Midterm Exam is a takehome, open-book exam. due Tuesday Feb 12 (in TA's mailbox by 4:30pm), available here; here are the Midterm solutions. Otherwise, no homework this week.

No class Monday Feb 11.


Week of February 18

Monday Feb 18 is a University holiday; no class.

Reading: Chapter 5 (Magnetism).

Homework set 5: Due Tuesday Feb 19: Jackson Chapter 3 (pp135ff) 3.7, 3.22. Jackson Chapter 4 (pp169ff) 4.1, 4.6ac, 4.7ab. Solutions 5 are available here.

No class Wed Feb 20; professor is out of town.


Week of February 25

Reading: Chapter 5 (Magnetism); begin Chapter 6.

Homework set 6: Due Tuesday Feb 26. Jackson Chapter 4 (pp169ff) 4.12. Jackson Chapter 5 (pp225ff) 5.3, 5.6. Solutions 6 are available here.


Week of March 3

Reading: Chapter 6 (Maxwell's Eqns).

Homework set 7: Due Tuesday Mar 4. Jackson Chapter 5 (pp225ff) 5.13, 5.22, 5.25ab, 5.26, 5.29. Solutions 7 are available here.
Hint on problem 5.29 The key point is to relate the solution of the electric problem to the solution of the magnetic problem. We assign test voltages V_1 and V_2 to the conductors, and then the electric problem can be solved by an electrostatic potential φ which obeys these boundary conditions. Now turn to the magnetic problem: we assume that the skin depth is small (see sect 5.13) so that the current flows on the surface. Use cartesian coordinates (x,y,z) with the conductors parallel to the z direction. Since all currents flow in the z direction only, the vector potential will have only a nonvanishing z-component A_z. Lo and behold, we can construct a solution to the magnetic problem just by setting A_z=φ: Taking the curl of A, we find that B obeys the proper boundary conditions at the surface. Furthermore we find that the surface current is equal to the electrostatic surface charge times some constant (with the dimensions of speed). Thus, throughout space outside the conductors, the E and B fields are equal in magnitude (times a constant), and perpendicular in direction. By writing down the definitions of mutual capacitance and mutual inductance in terms of the fields, the required result LC = const. follows.


Week of March 10

Reading: Chapter 6 (Maxwell's Eqns); begin Chapter 7 (Waves).

Homework set 8 (and last): Due Thursday Mar 13. Jackson Chapter 6 (pp283ff) 6.3, 6.4, 6.5, 6.11, 6.15. Solutions 8 are available here.
Hint on 6.4: Ohm's law in a moving conductor takes the form J = sigma(E + v cross B) because free charges experience a force proportional to that (or, you can appeal to Eq.5.142).


Week of March 17

Final Exam was a 24hr open-book take-home exam, from noon Tue Mar 18 to noon Wed Mar 19, available here. It covered the Introduction, and Chapters 1-6, with the basic ideas of Sects. 7.1-7.4. Solutions available here. Class average was 73/80.


dme 03/31/08