This is the syllabus for the graduate PHY 387 K class Electromagnetic Theory (I) as taught in Spring 2022 by Professor Vadim Kaplunovsky (unique number 56080). Note: this class may differ from the 387 K classes taught in past or future semesters.

Although the EMT class was originally scheduled to be in the face-to face mode, the current δ+ο wave of the covid-19 epidemic forced a change of plans. In particular, for the first two weeks (January 19 through 28) I shall teach on-line via Zoom. After that, from January 31 till the end of the semester I expect to teach teach in the hybrid mode. That is, I should teach in the classroom — and I encourage all healthy students to come to the class in person, — but the lectures will be mirrored via Zoom with videos archived on Canvas. However, all my plans are subject to change according to the epidemiological situation and the UT administration's desisions.

Meanwhile, please follow all the covid–19 safety measures. In particular:

- If you are not yet vaccinated, please
**get vaccinated as soon as possible!**The UT Health Service provides free vaccinations to all UT students (as well as many other people), and there are many other places in Austin where you can get your shot. Also, if you were vaccinated more than 6 months ago, get a booster shot. *If you are sick, do not come to the campus but stay home.*Or if you feel real bad, go see a doctor.- Please wear a face mask while indoors, especially in the classroom. The CDC recommend everybody — including the fully vaccinated people — to wear a mask indoors.

For your information, I am vaccinated (3 shots of Pfizer vaccine, including the booster shot). I shall wear a mask most of the time I am in class, but I might take it off for a minute now and then, so for your own safety, please do not sit too close to the lectern.

The main textbook for the class is Classical Electrodynamics by John David Jackson,
3^{dr} edition (1989).
If you already have an earlier edition of the book, you may use it as it contains similar physics, but beware:
The first two editions use Gauss units throughout the book, while the third editions (and hence my class) uses
MKSA units in the first 10 chapters.
Also, different editions have slightly different arrangements of subjects by chapters and sections, different
numberings of examples and problems, etc., etc.

Besides the textbook, I shall occasionally write my own supplementary notes or download them from the Internet. All such notes will be linked to this page (http://www.ph.utexas.edu/~vadim/Classes/2022s/notes.html).

The formal prerequisite for the Electromagnetic Theory (I) class is the graduate standing. The undergraduate students who have already taken the 352 K and 352 L classes are welcome to audit the class, but please talk to me before you take it for credit.

Since 387 K is a graduate class, I presume the students have already learned the undergraduate-level
electromagnetic theory — a freshemen E&M class followed by at least a semester of upper-division
*electrodynamics*.
But of course, it's your knowledge I care about, not the classes you have formally taken.
So please read Introduction to Electrodynamics by David Griffith: If you alreade know
and understand everything in the first 7 chapters of that book, you are ready for the graduate 387 K
class.
But if you have hard time with the undergraduate-level Griffith's book, then I suggest you take or audit
the undergraduate 352 K class before progressing to the graduate 387 K class.

Math-wise, I expect the students in my class to be fluent in vector calculus and have basic knowledge
of partial differential equations and complex analysis.
If you are unfamiliar with complex analysis, get an introductory textbook and start reading;
I suggest *Complex Variables* in the *Schaum Outlines* series,
by Spiegel, Lipschutz, Schiller, and Spellman; the PMA library has a few copies.
Please try to get through the first 7 chapters by the Spring break.

The graduate Electromagnetic Theory is a two-semester class sequence: The 387 K class covers the first 10 chapters of the Jackson's textbook (with an emphasis on chapters 6–10), while the 387 L class covers the rest of the textbook. Back when the course catalog was written (before the current students were born) both classes were required, but nowdays only the first half is required while the second half is optional. Accordingly, the required 387 K class is taught every semester while the optional 387 L class is taught on a rather irregular schedule, roughly one in a couple of years. But if you are interested in the subject, you should take both half of the Electromagnetic Theory course.

This semester I am teaching the 387 K class, and I have no idea who — if anybody — is going to teach the 387 L class next academic year. Accordingly, the course content below covers only the 387 K class I am teaching this Spring:

- Highlights of electrostatics and magnetostatics (Jackson chapters 1–5):
- Green's functions; electric and magnetic multipole expansions; dielectrics and the
**D**field; magnetic materials and the**H**field; boundary problems; electric and magnetic energies. - Maxwell equations and conservation laws (chapter 6):
- Maxwell equations; the potentials Φ and
**A**and the gauge transforms; EM wave equations; the continuity equation; the EM energy, its flow, and the Poynting theorem; linear momentum of the EM fields and the EM stress tensor; geometic symmetries of the EM fields. - Plane EM waves (chapter 7):
- Linear and circular polarizations; refraction and reflection; dispersion; phase and group velocities; dissipation.
- Wave guides and resonant cavities (chapter 8):
- Field equations and boundary conditions; modes in rectangular and cylindrical waveguides; imperfect conductors and attenuation; resonant cavities and their Q-factors.
- Radiation of EM waves (chapter 9):
- EM Green's functions; radiation by harmonic currents; multipole expansion; electric dipole radiation; higher multipoles and multippole expansion; radiation by atoms and nuclei; antennas.
- Scattering and diffraction (chapter 10):
- Scattering by small bodies; scattering in gases and liquids; scalar diffraction theory; diffraction off a sphere and in a circular hole; diffraction of the vector EM fields.

This class has 3 hours of regular lectures each week: 2 to 3 PM, in room RLM 5.112. The lectures will be shadowed on line via Zoom at https://utexas.zoom.us/j/95857239450 and archived on Canvas.

**Update 1/5:** As requested by the UT president Jay Hartzell, the first two weeks of classes
(January 18–28) will be online-only.
After that (Starting 1/31), the lectures will move to the classroom, although they will be shadowed online.
At that point, I strongly encourage all the *healthy* students to join me in class in-person.

Besides the regular lectures MWF 2 to 3 PM, I shall give make-up, likbez, and extra lectures. All such additional lectures will be on Mondays, from 4 to 5 PM (and hour after the regular Monday lecture), in room PMA 7.112, and mirrored via Zoom at https://utexas.zoom.us/j/93202114390.

The *make-up* lectures will replace the canceled regular lectures (such as 2/4).
They will cover the regular class material, and all the students should attend them.

The *likbez* lectures (named after Soviet 1920–40 program for elimitating illiteracy) are aimed at
plugging unecpected holes in undergraduate education.
They will cover the subjects that should have been well taught in the undergraduate school, but
somehow was not learned by some of the students.
The students who already know these subjects do not have to come to the likbez lectures, but the
rest of the students are strongly encourage to attend them.

Finally, the *extra* lectures — which I expect to give roughly every other week —
will be about subjects that are somewhat ouside the main focus of the course but are
interesting for their own sake, such as magnetic monopoles or superconductivity.
The students are strongly encoraged to attend the extra lectures,
but there is no penalty for missing them.
The issues covered by extra lectures will not be necessary
to understand the regular lectures and will not appear on exams.

Here is the *tentative* schedule of the make-up, likbez, and extra lectures:

- Likbez lecture on
**1/24**:*Separation of variables in detail*.

This lecture is online-only, at unusual time 3–4 PM and Zoom link https://utexas.zoom.us/j/94188193603. - Make-up lecture on
**2/7**:*Dielectric and magnetic materials*(regular class subject). - Extra Lecture on
**2/14**:*Classical and quantum motion of a charged particle*. - Extra Lecture on
**2/28**:*Electric-magnetic duality and Dirac's magnetic monopoles*. - Extra Lecture on
**3/7**:*Superfluids and Superconductors: Landau–Ginzburg theory, Meissner effect*. - Make-up lecture on
**3/28**:*Rectangular and circular waveguides*(regular class subject). - Extra Lecture on
**4/4**:*Superconductivity (II): magnetic vortices, type I and type II supperconductors*. - Extra Lecture on
**4/18**:*Superconductivity (III): Josephson junctions*. - Extra Lecture on
**5/2**:*SQUIDs and Aharonov–Bohm effect*.

For students' convenience, I shall keep a log of lectures and their subjects on this page (http://www.ph.utexas.edu/~vadim/Classes/2022s/lecturelog.html). Since the pace of the course may change according to the students' understanding, I will not make a complete schedule at the beginning of the class. Instead, I will simply log every lecture after I give it. This way, if you miss a lecture, you will know what you should read in the textbook and other students' notes.

The grades for this class will be based on the homeworks and the final exam; there will be no midterm exams. The homeworks (12 best out of 14) contribute 50% of the grade, the final exam the other 50%.

Besides affecting your grades, the homeworks are absolutely essential for understanding the course material.
Often, due to the time pressure, I will explain the general theory
in class and leave the examples for the homework assignment.
It is extremely important for you to work them out by yourselves;
otherwise, you might think you understand the class material but you would not!
*Be warned: The homeworks will be rather hard.*

I shall post homework assignments roughly once a week and post them (or rather link them) to this page. The solutions will be linked to the same page after the due date of each assignment.

I shall collect the homeworks in class on the day they are due.
If you cannot come to class for some reason, please scan your homework (or take *clear* pictures with your phone)
and email them to me and to the TA.

The final exam is scheduled for May 13 (Friday), 9–12 AM, in room JES A205A. Unlike the regular classes, the exam cannot be taken on-line; you must physically come to class on the exam day. If you are sick, or have other kind of emergency preventing you from coming to the exam, please let me know ASAP and I'll work out an alternative arrangement.

The final exam will be comprehensive — it may include any subject taught in class from the first lecture to the last (but not the extra lectures). During the exam, you may use open books and/or notes. However, if your books or notes are in electronic form, they must be downloaded before the exam. To make sure your exam is your own work, the Internet connection on all laptops, tablets, etc., must be turned off during the exam, and the cellphones must be completely turned off.

Instructor: Professor Vadim Kaplunovsky.

- Office: PMA 9.314A, office phone (512) 471–4918.

Alas, because of the covid-19 epidemic, I would come to the office only on the days I am teaching in-person, and only after the class. - Email: vadim@physics.utexas.edu.

Please use email for*simple*homework questions or administrivia. Complicated physics questions should be asked in person or via Zoom. - Virtual office hour: Thursdays, 2 to 3:30 PM, via Zoom at
https://utexas.zoom.us/j/96522049247.

Make sure to login to Zoom with your UT EID, here are the instructions how to do this. - If you need to reach me in a hurry, please email me your Skype ID or your WhatsApp number — or your phone number if you don't need the video link — and I'll call you back as soon as I can. Or catch me in the classroom right after a class.

Teaching assistant and grader: Asad Hussain.

- Email: asadh@utexas.edu.
- Office (after the first two weeks): Seventh floor graduate lounce (PMA 7.306).
- Hours (after the first two weeks): Wednesdays, 11:30 AM to 1:30 PM.

Last Modified: April 13, 2022. Vadim Kaplunovsky

vadim@physics.utexas.edu