Electricity and Magnetism

"I have also a paper afloat, with a electromagnetic theory of light which, till I am convinced of the contrary, I hold to be great guns."

Welcome to Physics 351! In this class we will study charges, currents, electric and magnetic fields, and their interactions. Much of the physics is expressed in a single, remarkable set of equations

\begin{gather} \vec{\nabla} \cdot \vec{E} = \frac{1}{\epsilon_{0}} \rho \vphantom{\frac{\partial\vec{B}}{\partial t}} \\ \vec{\nabla} \times \vec{E}\,= - \frac{\partial\,\vec{B}}{\partial \,t} \\ \vec{\nabla} \cdot \vec{B} = 0 \vphantom{\frac{\partial\vec{B}}{\partial t}}\\ \vec{\nabla} \times \vec{B} = \mu_{0}\,\vec{J} + \mu_{0}\,\epsilon_{0}\,\frac{\partial\,\vec{E}}{\partial\,t} \end{gather}

This formulation of electromagnetism is due primarily to the Scottish physicist James Clerk Maxwell. His equations, in one form or another, describe phenomenon ranging from the propagation of light to the deflection of a compass needle by a magnetic field.

James Clerk Maxwell (1831-1879)

The impact of Maxwell's equations extends well beyond electromagnetism: the Theory of Special Relativity is secreted away inside them, and they are the prototype for a unified description of the basic forces of Nature.


Basic information about our schedule, homework assignments, grades, and more can be found below. Click here to download a pdf version of the full syllabus. The syllabus has more detailed information, and you should be familiar with the policies and rules it describes.

Fall 2015 Schedule

We will cover most of the first nine chapters of the textbook, except for parts of chapters 8 and 9. The table below is an estimate of how we'll spend our time.

Week Dates Chapter
1 August 25, 27 1
2 September 1, 3 1, 2
3 September 8, 10 2
4 September 15, 17 2
5 September 22, 24 2, 3
6 September 29, October 1 3
7 October 6, 8 Mid-Semester Break, 3
8 October 13, 15 3, 4
9 October 20, 22 4, 5
10 October 27, 29 5
11 November 3, 5 5
12 November 10, 12 5, 6
13 November 17, 19 6, 7
14 November 24, 26 7, Thanksgiving Break
15 December 1, 3 9

Please keep in mind that these dates are subject to change. There are two reasons for this. First, I usually teach this course in the spring. The fall calendar is different and it may require some changes. Second, I may decide to switch things around or spend more or less time on a given chapter. I will always notify you about any changes I make to this schedule.


Homework is assigned each week and collected the following week. Only some of the problems from each assignment will be graded. I won't tell you which ones, so you need to complete all the problems. Current and past assignments are listed below. Solutions are available for some (not all) problems, but I am no longer making them available for download — please stop by my office if you'd like to see the solutions for a particular assignment.

Assignment 6
Method of Images
Due on October 9

This is the first homework for Chapter 3, with problems that address the “method of images”.

Assignment 5
Electrostatic Potential Energy
Due on September 24
Correction: Changed ‘quadratic’ to ‘linear’ in Problem 3

Homework 5 covers electrostatic potential energy, as well as some common features of \(1/r^{2}\) forces.

Assignment 4
Electrostatic Potential
Due on September 17

This is the second homework for Chapter 2, covering the electrostatic potential. Notice the question at the end of problem 6, after you calculate the potential.

Assignment 3
Due on September 10

This is the first homework for Chapter 2. The rules about using Mathematica and similar tools are stated at the top of the assignment. (They are not allowed, just like on the last assignment.)

Assignment 2
More Vector Analysis
Due on September 3

This assignment covers the rest of our Math Methods review. Read the instructions at the top of the page -- Mathematica and similar tools are not allowed!

Assignment 1
Review of Vector Analysis
Due on August 25

This assignment is due at the beginning of the first class. It is a review to get you up-to-speed on some aspects of vector analysis that we will frequently use in class.

Working with your classmates on these assignments is encouraged! But you should only hand in work that you've completed on your own. If your solution looks just like someone else's work then you need to go back and redo it from scratch. If you can't explain each step of your solution then you haven't completed the problem on your own. Remember: the only way to be ready for the exams is to do the homework yourself.

A Warning

Never, ever hand in an assignment that has been copied from a solutions manual. You won't learn anything that way, and it will earn you a grade of zero for that assignment. If it happens more than once it will be reported to the Department Chair and the Dean. Consider yourself warned. Click here to see the College of Arts and Sciences Statement on Academic Integrity.


Grades in the course are primarily determined by homework assignments and exams. The weekly homework grades contribute 35% of your final grade in the class, and two “midterm” exams (dates TBA) count 15% each. A cumulative final on Friday, December 11 (from 1:0-3:00 PM) is worth 30%. The remaining 5% depends on attendance and participation. Asking questions, taking advantage of office hours, and attending both lectures and discussion sections will earn you the full 5%. Check the pdf syllabus for more details.


The main text for the class is Introduction to Electrodynamics by Griffiths. The tone of the book is casual and most students find it very accessible. When I was an undergraduate I used the the books by Wangsness and Purcell. Those texts might be useful if something in Griffiths isn't clear. A more advanced treatment is given in Jackson's Classical Electrodynamics, which is the text for practically every graduate E&M course.

  1. Introduction to Electrodynamics
    David J. Griffiths
  2. Electromagnetic Fields
    Roald K. Wangsness
  3. Electricity and Magnetism
    Edward M. Purcell
  4. Classical Electrodynamics
    J.D. Jackson

Griffiths' book has a very complete (for our purposes) discussion of vector calculus as it is used to describe electricity and magnetism. If you'd like to see additional discussions of this material, I recommend the math methods book by Boas, and also the book by Riley, Hobson, and Bence. For a more advanced treatment refer to Arfken and Weber.

  1. Mathematical Methods in the Physical Sciences
    Mary L. Boas
  2. Mathematical Methods for Physics and Engineering
    K.F. Riley, M.P. Hobson, and S.J. Bence
  3. Mathematical Methods for Physicists
    George Arfken and Hans Weber

From time to time I may supplement the material from the book with my own notes, which will be posted below.


A Tricky Integral
One of the problems on Assignment 4 leads to an integral of the form \begin{gather} \int dx\,\sqrt{x^2 + \alpha^2} ~. \end{gather} Evaluating this integral requires the application of several different integration techniques, including changes of variables, trig substitutions, and the method of partial fractions.

A Few Useful Integrals
A quick review of how to evaluate a few integrals that show up again and again on the homework.

Line Integrals

This is a very basic review of line integrals -- what they are, how to evaluate them, etc. It may be useful if you're a little rusty on this topic. The file is big (about 22 MB) because of the various plots. Let me know if you find any typos or mistakes and I will post a corrected version.

E&M Stress Relief

Sometimes the E&M wears you out, and you need a picture of an adorable little kid doing physics to get you back on track. Not a problem.