PHYS 405: Electricity and Magnetism I

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

Teaching assistant
Loc Ngo
Office: PAIS 3414

Description of the class

 The goal of this class is to introduce the subject of classical electromagnetism at the advanced undergraduate level. Classical electromagnetism (EM) is fundamentally a local theory of vector fields and its proper treatment requires methods of vector analysis and differential equations. We will briefly review these mathematical concepts in the first few lectures of the class. In this class, we will entirely focus on static (time-independent) fields interacting with charges at rest or in steady motion. In this case, the electric and magnetic fields decouple from one another so they can be treated independently. Such independent treatment of electrostatics and magnetostatics is the central content of this class.

 A sizable fraction of this class will be spent computing the electric field and potential created by a static distribution of charges. We will also discuss how the electric field behaves within conductors and insulators. The second part of the class will be spent computing magnetic field resulting from static currents, including how the magnetic field behaves in the presence of insulating matter. Time-dependent electric and magnetic fields created by moving charges and nonsteady currents will be covered in the next Electricity and Magnetism course, PHYS 406.


The detailed syllabus can be found here.


Mondays and Wednesdays, 8:30-9:45am 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 1-6.

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

Office hours

Tuesdays and Wednesdays 1:00-2:00pm at my office PAIS 3214 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 Fridays 10-11am for you to come by in PAIS 3414 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. Attendance/Class participation will count for 10% of the final grade.
  2. Homework: there will be 9 assignments, which will represent the 25% of the final grade.
  3. Two midterm exams: each of them will represent the 20% of the final grade.
  4. Final: will represent the remaining 25% of the final grade.

The midterm exams are tentatively scheduled for February 22 and April 12 during class time, and the final exam will be held during exam week on May 10 12:30pm.

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 at my office on the day they are due. Late Homework assignments will be accepted but with a 25% penalty for each day past the deadline. So a homework handed-in within 24 hrs of the deadline will carry a 25% penalty, one handed-in within 48 hrs will carry a 50% penalty, as so on. Let me know if you are planning on submitting your homework late such that I can delay the posting of the solutions. 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 415, this is a very important adjunct to the main lecture class, taking place every Wednesday from 4 to 4:50pm 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 Tuesday 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.

Syllabus topics

You can find the calendar for the course in the tentative schedule.

  1. Electrostatics
    - Electric field
    - Electric potential
    - Electrostatic work and energy
    - Conductors
  2. Boundary value problems in electrostatics
    - Laplace's equation
    - The method of images
    - Separation of variables
    - Multipole expansions
  3. Electric field in matter
    - Bound charges and electric polarization
    - Electric displacement field
    - Linear dielectrics
    - Energy in dielectrics
  4. Magnetostatics
    - Lorentz force
    - Biot-Savart and Ampere laws
    - Correspondences between electrostatics and magnetostatics
    - Magnetic vector potential
  5. Magnetic fields in Matter
    - Magnetic dipoles and magnetization
    - Magnetic field of a magnetized object
    - Magnetic media

Tentative schedule

Date Lecture Notes Griffiths Reading Homework HW Due Solutions
Week 1
No Class 01/16: MLK Day
Vector algebra review
Ch. 1.1-1.3
Homework 1
Homework 1 Solutions
Week 2
Gradient operator and its fundamental theorem
Divergence, curl, and their theorems
Ch. 1.2-1.6

Week 3
Spherical and cylindrical coordinates
Helmholtz-Hodge decomposition
Electromagnetism intro
Electric field
Square Loop example

Ch. 2.1-2.2
Homework 2
Homework 2 Solutions

Week 4
1D Dirac Delta function
3D Dirac delta function
Gauss's Law
Curl of E and electric potential
Ch. 2.3-2.4
Homework 3
Homework 3 Solutions
Week 5
Work and energy in electrostatics
Boundary conditions and conductors
Ch. 2.4-2.5

Week 6

02/22: Midterm #1
Ch. 2.5

Week 7
Forces on conductors and capacitance
Laplace's Equation
Ch 2.5-3.1
Homework 4
Homework 4 Solutions
Week 8
The method of images
Direct solution to Laplace's equation in cartesian
Ch 3.1-3.3

Week 9
Spring Break: No Class

Week 10
Direct Solution to Laplace's equation in spherical coordinates
Spherical coordinate examples and direct solutions in cylindrical coordinates
Ch. 3.3
Homework 5
Homework 5 Solutions
Week 11
The multipole expansion
Torque and Force on dipoles
Ch. 3.4-3.5, 4.1
Homework 6
Homework 6 Solutions
Week 12
Electric field within matter
Bound charges and polarization
The electric displacement field and linear dielectrics
Ch. 4.1-4.4

Week 13
Dielectrics and Capacitance
Review of Chap. 3
04/12 Midterm #2
Ch 4.4

Week 14

Magnetic Force vs Electric Force
Ch. 4.4, 5.1
Homework 7 04/24
Homework 7 Solutions
Week 15

The Biot-Savart Law
Magnetic field from simple objects
Maxwell's equations for magnetostatics
The vector potential
Ch. 5.2-5.4
Homework 8
Homework 8 Solutions

Week 16
Multipole Expansion for the vector potential
Magnetic field in matter
Ch. 6.1-6.4
Homework 9
Homework 9 Solutions

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
02/15 Problems #5
Problems #5 Solutions
Peer-review of Midterm 1

Problems #6
Problems #6 Solutions
Problems #7
Problems #7 Solutions
Spring Break

Problems #8
Problems #8 Solutions
Problems #9
Problems #9 Solutions
Problems #10
Problems #10 Solutions
Peer-review of Midterm 2

04/19 Problems #11
Problems #11 Solutions
04/26 Problems #12
Problems #12 Solutions
Problems #13
Problems #13 Solutions