# Classical ElectroDynamics

Classical Electrodynamics is an upper-division course for Physics students. In a perfect world it would be a single year-long class, but for administrative reasons it is split into two separate classes taught by different professors:

• 352 K — Classical Electrodynamics (I) — a required class offered every long semester.
• 352 L — Classical Electrodynamics (II) — an optional class offered in Spring semesters only.
Physics-wise, the split is rather arbitrary, so if you want to be a physicist, you should take both of these classes!

This document is the syllabus of the Classical Electrodynamics (I) class as taught by Dr. Vadim Kaplunovsky in the Spring of 2024, unique number 56055.

## Textbook

The textbook for the 352 K class is Introduction to Electrodynamics by David J. Griffith, 4th edition. This textbook is required — I shall use the problems in the book as homeworks.

The 352 K class will focus on textbook chapters 1 through 7. The remaining chapters 8 through 12 will be covered in the 352 L class.

### Supplementary notes

Besides the Griffith's textbook, I shall not use any supplementary textbooks in my class. Instead, I shall sometimes write my own supplementary notes or use some material on the Internet. The links to all such supplementary notes will be posted to this web page.

## Course Content

### Classical Electrodynamics (I)

Math of vector fields:
Gradient, divergence, curl, and relations between them; second derivatives; line, surface, and volume integrals; fundamental theorems; delta-functions; differential equations for the fields.
Electrostatics:
The electric field and its divergence and curl; Gauss law and its uses; electrostatic potential and the Poisson and Laplace equations; boundary conditions; electrostatic energy; conductors and surface charges.
Solving the Laplace equation for the potential:
Boundary conditions; image charges; separation of variables method; multipole expansion.
Electric fields in matter:
Polarization of dielectrics; induced dipole moment; electric displacement field D; fields and energies in dielectric systems; forces on a dielectric.
Magnetostatics:
Magnetic field and its divergence and curl; magnetic forces; Biot–Savart–Laplace law; Ampere law; the vector potential.
Magnetic fields in matter:
Diamagnetic, paramagnetic, and ferromagnetic materials; induced magnetization; the H field and the Ampere law; linear and non-linear materials.
ElectroDynamics:
Ohm law and EMF; electromagnetic induction; Faraday's law; Maxwell's equations.

### Classical Electrodynamics (II)

Conservation Laws:
Continuity equation and conservation of the electric charge; Poynting vector and the EM momentum; EM work and energy; EM pressure and stress tensor.
Electromagnetic Waves:
Waves and the wave equation; EM waves in vacuum; EM waves in matter; absorbtion and dispersion; guided EM waves.
Electromagnetic potentials:
Scalar and vector potentials; gauge transforms; potentials of continuous charges and currents; potentials of moving point charges.
Electrodynamics and special relativity:
Special relativity; relativistic mechanics; relativistic EM fields; Lorentz transforms of potentials and fields; 4–vectors and tensors.

## Prerequisites

The Classical Electrodynamics classes are intended for the upper-division Physics students who have already completed the lower-division Physics class sequence 301–316–315–319 (plus the corresponding labs) as well as Mathematics class sequence 408 C+D and 427 K+L (or any of the equivalent math classes). These are not just the formal prerequisites — you would really need that knowledge to follow the upper-division Physics classes.

The formal prerequisites — checked by the registrar computer — for the 352 K class are Math 427 L or 364 K and Physics 315 and 115, all with grades no worse than C−. Please note that I have no authority to waive these prerequisites!

If you have taken the prerequisite classes outside the UT, or if you have any other kind of prerequisite or registration problem, please go your advisor or to one of the undergraduate coordinators at the Physics departement:

Melva J Harbin:
Jonathan Pereira:

## Logistics

Instructor:

### Lectures

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: 2 to 3:30 PM on Tuesdays and Thursdays, face-to-face in room PMA 7.104, Zoom mirror at https://utexas.zoom.us/j/98026699252.

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

#### Extra Lecture(s)

Besides the regular lectures, I plan to give one or two extra lectures about subjects that are somewhat outside the main focus of the course but are interesting for their own sake, such as Aharonov–Bohm effect or magnetic monopoles. 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 in homeworks or exams.

The extra lectures — and also the make-up lectures for the caneled classes — will be on Fridays, from 4 to 5 (or 5:30 ) PM, room TBA, Zoom mirror at https://utexas.zoom.us/j/92691007833. Here is the tentative schedule:

• Make-up Lecture on 1/26: Vector calculus and its applications to electrostatics, 4 to 5:30 PM, in the regular classroom PMA 7.104.
• Extra Lecture on 4/5: Quantum charged particles and Aharonov–Bohm effect.
• Extra Lecture on 4/19: Electric-magnetic duality and Dirac monopoles.

#### Lecture Log and Scans

For students' convenience, I shall keep a log of lectures and their subjects on this web page. Since the pace of the course may change according to the students' understanding, I shall not make a complete schedule at the beginning of the class. Instead, I shall 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 Zoom mirrors of all lectures — video and audio — should be recorded on the claud and become available to the students via Canvas after a short delay. To find the recording, login to Canvas, select this class, then select Zoom: on that page, you should get a list of all the recorded lectures. But if due to some technical glitch a llecture does not get recorded, I shall scan the notes I have used in class and links the scans to this page.

#### Review sessions:

This class will have 3 exams: 2 midterm exams, and 1 final exam. Before each exam, the TA will give a review session, in which he will solve a few exam-like problems (but do not expect him to solve the actual exam problems) and answer your questions.

Here is the schedule of the review sessions:

• Review before the first midterm: February 22 (Thursday), from 5 to 5:30 PM, in room PMA 5.120.
• Review before the second midterm: April 2 (Tuesday), from 5 to 6:30 PM, room TBA.
• Review before the final exam: April 29 (Monday), time and room TBA.

The grades for this class will be based on combined scores of the homeworks, the midterm exams, and the final exam.

• 20% of the average of 10 best homework sets (out of 12 sets total).
• 20% for each of the two midterm exams (40% altogether).
• 40% for the final exam.

The brackets for converting the combined HW+MT+FIN scores into letter grades will be set after the final exam.

### Homework

Homework is essential for learning any difficult material. Often after listening to a lecture and/or reading the textbook you may feel like you know the material, but to make this knowledge useful you must learn how to actualy apply it to solving problems, and that's what the homework is for. Without doing the homework, you will never master any Physics or Math; at best, you might «have heard something about it».

To encorage you to do your homework for this class, it will comprise 20% of your grade. There will be 12 largish homework sets over the semester; 10 best sets will count towards your grade. To allow for illness or emergencies, you get to drop two worst (or missing) sets.

I shall not post the homework assignments to Canvas; instead, I shall post them to this web page (http://www.ph.utexas.edu/~vadim/Classes/2024-u/homework.html). Most of the problems will be taken from the Griffith's textbook, but sometimes I'll add a few problems of my own.

I shall collect the homeworks in class and give them to the TA to grade. If you cannot come to the class for any reason, put it in electronic form* and email it to me and to the TA before 5 PM on the day the homework is due. Please do not waste time asking my permission to submit your homework electronically, just scan it and email it. And do not try to submit your homework via Canvas; if you do it would probably get lost.

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

Your homework should make clear what are you trying to do and why. Please comment your formulae (unless they are obvious). This way, if you make mistakes you would still get partial credit for trying to do the right thing.

Once the homeworks are collected I shall post the solutions and link them to the homework web page.

### Exams

This class has two midterm exams and one final exam at the end of the semester. Each midterm contributes 20% to your grade, and the final exam is worth 40% of the grade.

The midterm exams are taken in class — at the regular class time in the usual classroom.

• The first midterm is on February 27. Subjects: textbook chapters 1, 2, and most of chapter 3.
• The second midterm is on April 4. Subjects: end of textbook chapter 3, and whole chapters 4 and 5.

The final exam is tentatively scheduled for May 3 (Friday), 10:30 AM to 12:30 PM, room TBA. The final exam is comprehensive and covers the whole course, from the first lecture to the last, or in textbook terms, everything in chapters 1 through 7.

All the exams must be taken in-person, you cannot take them via Zoom.

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.

Unlike the homeworks, you do not get to drop any midterm or final exams. If you miss an exam because of a documented illness or emergency, please let me know as soon as possible, and I'll work out an appropriate remedy. But if you miss an exam for any other reason, you would be SOL and your grade would suffer.

However, I shall allow students to take their exams ahead of the regular exam date in case of schedule conflicts. If you know ahead of time that the exam date and time conflicts with another exam, a pre-scheduled UT event you must participate in, a religious holiday you observe, a job interview, or with any other commitment, — please contact me two weeks ahead of time so I can reschedule your exam to a mutually convenient date and time.

Likewise, the students who need extra time to complete their exams due to a disability, please contact me two weeks before the exam to set up the time and the place for your test.