Electricity and Magnetism

"I have also a paper afloat, with an 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.

Fall 2017 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 29, 31 1
2 September 7, 7 1, 2
3 September 12, 14 2
4 September 19, 21 2
5 September 26, 28 2, 3
7 October 3, 5 3
8 October 10, 12 Fall Break, 3
9 October 17, 19 3, 4
10 October 24, 26 4
11 October 31, November 2 4, 5
12 November 7, 9 5
13 November 14, 16 5, 6
14 November 21, 23 6, Thanksgiving Break
15 November 28, 30 7
15 December 5, 7 9

Please keep in mind that these dates are subject to change. 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.

Assignments

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 8
The Multipole Expansion
Due on Friday, October 27

This is the last assignment for Chapter 3, covering the sections on the Multipole Expansion of the potential.

Assignment 7
Separation of Variables
Due on October 20

Separation of variables is a very important technique for solving the Laplace and Poisson equations. It is often dramatically easier than evaluating the integrals for $$V$$ and $$\vec{E}$$.

Assignment 6
Method of Images
Due on October 12

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

Assignment 5
Electrostatic Potential Energy
Due on September 28

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

Assignment 4
Electrostatic Potential
Due on September 21

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
Electrostatics
Due on September 14

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 7

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 29

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 exams (dates TBA) count 15% each. A cumulative final on Friday, December 16 (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.

References

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

The Feynman Lectures on Physics, which include a few nice discussions about some of the things we'll talk about in class, are available online. I will also place a copy of the lectures in Isaac & Al's.

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

Notes

These notes provide a detailed discussion of an example we worked out in class: the potential inside and outside a spherical shell with the azimuthally symmetric surface charge density $$\sigma(\theta) = \sigma_{0} \cos\theta$$. Please take a look, especially if you have questions about Assignment 7.

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

We didn't say much about the Dirac delta in class on 8/31/17, so I have written out some notes that you might find helpful when working on the homework.

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.