This is the syllabus for the graduate PHY 387 K class Electromagnetic Theory (I) as taught in Spring 2019 by Professor Vadim Kaplunovsky (unique number 55665). 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/2019s/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.

Back when the course catalog was written (before the current students were born), the graduate Electromagnetic Theory was a two-semester class sequence: The 387 K class covered the first 10 chapters of the Jackson's textbook (with an emphasis on chapters 6–10), while the 387 L class covered the rest of the textbook. Alas, our department could not offer the 387 L class in the last few years, it's not going to be offered this or next year and is unlikely to be offered before you finish your Ph.D.'s, — so 387 K is the only graduate E&M class you are going to take. Therefore, I made my own choice of the subjects I must teach in my class and skip the rest. I wish I could teach them all, but my class has only 3 hours per week for just one semester.

- 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.
- Radiation and scattering (chapters 9–10):
- EM Green's functions; radiation by harmonic currents; multipole expansion; electric dipole radiation; higher multipoles; antennae; radiation by atoms and nuclei; maybe multipole expansion of the radiated fields; scattering by small bodies; scattering in gases and liquids.
- Special Relativity (chapters 11–12):
- Einstein postulates; Lorentz transforms; 4–vectors; adding velocities; relativistic energy
and momentum; A
^{μ}potentials and F^{μν}fields; Lagrangian and Hamiltonian for a charged particle; particle motion in EM fields; maybe Lagrangian for the EM field; EM stress-energy tensor. - Radiation by moving charges (chapter 14):
- Liénard–Wiechert potentials; radiation by an accelerated charge; relativistic accelerated charge; synchrotron radiation.

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 (http://www.ph.utexas.edu/~vadim/Classes/2019s/homeworks.html). The solutions will be linked to the same page after the due date of each assignment.

*The homeworks are assigned on the honor system:*
I shall not collect or grade the homeworks, but you should endeavor
to finish them on time and check each other's solutions.

The grades will be based on *two take-home exams*, one in the middle of
the semester, the other at the end;
the mid-term exam contributes half of the grade and the end-term exam the other half.
There will be no in-class final exams.

- The mid-term exam will be given to students in late March and due a week later.
- The end-term exam will be given to students on May 9 (last class) and due on May 16.

This class has 3 hours of regular lectures each week: 3:30 to 5 PM on Tuesdays and Thursdays, in room RLM 5.120.

Besides the regular lectures, I shall give a few extra lectures 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.

The extra lectures will be on Wednesdays, here is the tentative schedule:

- Lecture on
**2/6**:*Classical and quantum motion of a charged particle*. - Lecture on
**2/20**:*Aharonov–Bohm effect and Dirac's magnetic monopoles*. - Lecture on
**3/6**:*Superconductivity (I): Landau-Ginzburg theory, Meissner effect*. - Lecture on
**3/27**:*Superconductivity (II): magnetic vortices, type I and type II superconductors*. - Lecture on
**4/17**:*Superconductivity (III): critical current; Josephson junctions*. - Lecture on
**4/24**:*Superconductivity (iV): SQUIDs*. - Lecture on
**5/7**:*Electric–magnetic duality*.

As to the time and the room,

- The first two extra lectures (2/8 and 2/20) are from 12 to 1 PM, in room RLM 9.222.
- The rest of the extra lectures are from 1 to 2 PM in room RLM 5.104.

For students' convenience, I shall keep a log of lectures and their subjects on this page (http://www.ph.utexas.edu/~vadim/Classes/2019s/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.

Instructor: Professor Vadim Kaplunovsky.

- Office location: RLM 9.314 A.
- Office hours: The students are welcome whenever I'm in my office and not too busy. The best times to look for me are Mondays 3-5, Wednesdays 3-4, and Thursdays 2-3.
- Email: vadim@physics.utexas.edu.

Please use email for*simple*homework questions or administrivia. Complicated physics questions should be asked in person. - Office phone: (512) 471-4918.

Teaching Assistant: Yuan-Pao Yang.

- Email: yjp1986@utexas.edu.
- Office: RLM 9.312.

Last Modified: April 18, 2019. Vadim Kaplunovsky

vadim@physics.utexas.edu