This is the syllabus for the graduate PHY 387 K class Electromagnetic Theory (I) as taught in Spring 2024 by Professor Vadim Kaplunovsky (unique number 56180). Note: this class may differ from the 387 K classes taught in past or future semesters.

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/2024s/notes.html).

The formal prerequisite for the Electromagnetic Theory (I) class is the graduate standing.

For the undegraduate students who have already taken the 352 K class and want to learn more electrodynamics, I strongly recommend taking the undegraduate 352 L class instead of my graduate class. The 352 L class — based on the second half of the Griffith's textbook — is both technically easier than the graduate 387 K class and also contains more interesting material (albeit at the less deep level). But if you have taken both 352 K and 352 L classes and look for a harder challenge, you are welcome to my graduate class.

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, whenever enough students ask for it.. 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 multipole 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 is officially face-to-face, but I plan to shadow all the lectures online via Zoom and have them recorded for asyncronous viewing via Canvas. I strongly encourage all students to come to the lectures in person, but if you are sick please stay home and watch the lecture online.

There are 3 hours of regular lectures each week: 3:30 to 5 PM on Tuesdays and Thursdays, face-to-face in room PMA 5.116, Zoom mirror at https://utexas.zoom.us/j/93204891099.

**Class on Tusday 1/16 is canceled** and will be made up.
The frst class this semester is on Thursday 1/18.

Besides the regular TTh 3:30 to 5 lectures, there are going to be make-up, likbez, and extra lectures on some Fridays from 4 to 5 (or 5:30) PM. All such lectures will be online-only, at Zoom link https://utexas.zoom.us/j/96411236825, (Note different Zoom link from the regular lectures.)

The *make-up* lectures will replace the canceled regular lectures, if any.
They will cover the regular class material, and all students should attend them.

The *likbez* lectures (named after Soviet 1920–40 program for elimitating illiteracy)
are aimed at plugging unexpected holes in the undergraduate education.
They will cover the subjects that should have been taught in the undergraduate school, but somehow were 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 the homeworks or the final exam.

Here is the tentative schedule of the make-up, likbez, and extra lectures for this semester:

- Make-up lecture on
**1/19**:*Separation of variables method*(regular class subject). - Extra Lecture on
**2/2**:*Classical and quantum motion of a charged particle*. - Extra Lecture on
**2/16**:*Electric-magnetic duality and Dirac's magnetic monopoles*. - Extra Lecture on
**3/1**:*Superfluids and Superconductors: Landau–Ginzburg theory, Meissner effect*. - Extra Lecture on
**3/22**:*Superconductivity (II): magnetic vortices, type I and type II supperconductors*. - Extra Lecture on
**3/29**:*Superconductivity (III): Josephson junctions*. - Extra Lecture on
**4/12**:*SQUIDs and Aharonov–Bohm effect*.

For students' convenience, I shall keep a log of lectures and their subjects on this page. 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 (11 best out of 13) 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, email^{*} your homework to me and to the TA before 6 PM
on the day the assignment is due.
Note: don't waste time asking my permission to submit your homework electronically, just do it!

* If you type your homework in LaTeX, Work, or whatever, email the PDF file. If you write it on paper, scan it (or take a clear picture with a document camera or a phone), put all pages into a single PDF file or a zip archive, and email that.

The final exam is *tentatively* scheduled for May 2 (Thursday), 3:30 to 6:30 PM, room TBA.
The exam is 3 hours long, and you must take it in person at the exam room: it cannot be taken online.
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-subject 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.
- Office hour: Wednesday 2:30 to 3:30 PM.
- 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. - 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.

Teaching assistant and grader: Grant Elliot.

- Email: gelliot123@utexas.edu.
- Office: PMA 9.202.
- Office hour: Thursday 11:30 AM to 12:30 PM.

Last Modified: January 22, 2024. Vadim Kaplunovsky

vadim@physics.utexas.edu