PHYS 406: Electricity and Magnetism II

Prof. Francis-Yan Cyr-Racine
Office: PAIS 3214

Teaching assistant
Loc Ngo
Office: PAIS 3414

Description of the class

This class builds on the foundation established in PHYS 405 to develop the complete theory of electrodynamics. Starting from Maxwell's equations for electrostatics and magnetostatics, we will see how these have to be modified to account for time-varying fields. Equipped with the time-dependent Maxwell's equations, we will be able to discuss the energy, momentum, and angular momentum contained within the electromagnetic field. We will then discuss the very important topic of electromagnetic waves and their propagation both in vacuum and within linear media. We will then argue that scalar and vector potentials are generally easier to handle than fields in electrodynamics, and will use this fact to compute the E&M signatures of moving point charges, including how they radiate energy in the form of electromagnetic waves. We will finally turn our attention to more fundamental aspects of electrodynamics, discussing its relativistic nature and its modern Lagrangian formulation, which reveals the fundamental symmetries underpinning the theory.

The Take-home Final Exam will take place on December 16-17.


The detailed syllabus can be found here.


Tuesdays and Thursdays, 11:00am-12:15pm in PAIS 1140.


Textbook for the class
Introduction to Electrodynamics (4th Edition) by D. J. Griffiths. Older editions of the book are likely fine as well. The course will cover Chapters 7-12.

Additional resource
Electricity and Magnetism by E. Purcell and D. Morin.

Office hours

Tuesdays and Thursdays  3:00-4:00pm at my office or on Zoom. These are my preferred "office" hours. If you can't make my regular office hours, or if your questions cannot wait, please send me an email to set up an appointment.

Teaching assistant
The teaching assistant is Loc Ngo ( He will be available on Monday 1-2pm at his office in PAIS 3414 for you to meet and discuss any homework grading issues you may have. If you need to schedule an appointment outside of the TA's office hours please send him an email.


The grading in the course will be based on your performance in homework assignments, two midterm exams, and a final exam. The contribution to the final grade is as follows:

  1. Class participation will be 10% of the final grade.
  2. Homework: 9 assignments will represent 20% of the final grade.
  3. Two midterm exams: each of them will represent 20% of the final grade.
  4. Final exam: will represent the remaining 30% of the final grade.

The midterm exams are tentatively scheduled for September 23rd and October 28th during (extended) class time, and the final exam will be held during exam week.

Homework assignments

There will be 9 assignments during the semester. The assignments will be posted in the tentative schedule about 7-10 days before they are due. The login information necessary to access the homework PDFs will be provided in the first class. The homework must be submitted to me in class the day they are due. Late homework policy: homework returned in the next 24 hours after the due date will be accepted but with 25% penalization (i.e. the maximum grade you can get in this case is 75% of the total points for that homework). After these 24 hours the corresponding solutions will be posted here, and homework assignments submitted after solutions post will not be graded.

While I strongly encourage you to discuss the homework assignments with your classmates, the work you hand in must be entirely yours.

Problems class

Listed officially as PHYS 416, this is a very important adjunct to the main lecture class, taking place every Thursday from 1 to 1:50pm in PAIS 1140. It will provide you additional practice with solving problems beyond the homework assignments and self study. Furthermore, the class will also give you a valuable opportunity to bring to my attention your difficulties with any concepts covered in the lecture class so I can address them in a group setting. The problem sheets would be posted here on the Wednesday before the problem class. The corresponding solutions will be posted after the class. You will receive credit for the problems class as long as you register and show up for more than 10 sessions. Even if you don't register for the class, I encourage you to attend anyway, just to get the extra practice.

Tentative schedule

Date Lecture Notes Griffiths Reading Homework HW Due Solutions
Week 1
Review of Electro- and Magnetostatics
Vector potential problem
Chs 1-6
Ch 7.1
Homework 1
Homework 1 Solutions
Week 2
Current, EMF, Faraday's law
Ch. 7.1-7.2

Week 3
Inductance, B-field Energy
Maxwell's equations in electrodynamics
Ch. 7.2-7.3
Homework 2

Homework 2 Solutions
Week 4
Matter Effects in Electrodynamics
Energy and Poynting theorem
Momentum in Electrodynamics
Ch 7.3-8.2
Homework 3

Homework 3 Solutions
Week 5
Review of Ch. 7 & 8
09/23: Midterm #1
Ch 8.2-8.3

Midterm 1 Solutions
Week 6
Intro to Electromagnetic Waves
Ch 9.2
Homework 4
Homework 4 Solutions
Week 7
Electromagnetic waves in matter
Brewster's angle
Ch 9.3
Homework 5
Homework 5 Solutions
Week 8
Electromagnetic waves in conductors
10/14: No class (Fall break)
Ch. 9.4

Week 9
Reflection at the surface of conductors
Dispersion of EM waves
Dispersion of a Gaussian wave packet
Intro to wave guides
Ch 9.4-9.5
Homework 6
Homework 6 Solutions
Week 10
Rectangular wave guides
TM mode and energy propagation in wave guides
10/28: Midterm #2
Ch 9.5

Midterm 2 Solutions
Week 11
Potentials and gauge transformation
Retarded Potentials
Ch 10.1-10.3
Homework 7
Homework 7 Solutions
Week 12
Liénard-Wiechert Potentials
Fields from a moving point charge
Ch. 10.3

Week 13
Four-vectors and the metric
Ch 12.2
Homework 8
Homework 8 Solutions
Week 14

Minkowski Force
11/25: No class (Thanksgiving)

Week 15

Electromagnetic Field Strength

Homework 9
Homework 9 Solutions
Week 16
Maxwell's equations from a Lagragian
How Fields transform

Problems class

Date Problems Solutions
Problems 1
Problems 1 Solutions
Problems 2
Problems 2 Solutions
Problems 3
Problems 3 Solutions
Problems 4
Problems 4 Solutions
09/23 Midterm peer review

Problems 5
Problems 5 Solutions
Problems 6
Problems 6 Solutions
No problem class (Fall break)

Problems 7
Problems 7 Solutions
Midterm peer review
Problems 8
Problems 8 Solutions
Problems 9
Problems 9 Solutions
Problems 10
Problems 10 Solutions
11/25 No problem class (Thanksgiving)

12/02 Problems 11
Problems 11 Solutions
Problems 12
Problems 12 Solutions