Fall 2025
Email is the best way to contact me. Many questions and issues can be solved over email.
I will be in my office
| Monday | 9:00–10:00 |
| Tuesday | 11:00–12:00 |
| Tuesday | 1:00– 2:00 |
| Wednesday | 9:00–10:00 |
| Friday | 9:00–10:00 |
during the course of the Fall 2025 semester.
If you need to meet at a different time, please send me an email to set that up. You can drop by my office any time to see if I am there. If I’m there, we can chat.
This is the first in a two-course sequence of electromagnetic theory required in the physics major at Lebanon Valley College. PHY 321 is a 3-credit course. PHY 321 contains 3 contact hours of instruction per week.
What role does electromagnetic theory play in physics? This is a good and important question. We know that electricity is part of physics, but maybe it seems that it’s a peripheral part, a sort of side topic like the theory of sound. This is completely wrong.
Electromagnetic theory is central to physics. At the center. At the core. Why?
Today’s physicists believe that all known interactions come down to four forces. These are
What about friction and tension? They are electromagnetic at a micro level. All of chemistry is based on the electromagnetic force. That doesn’t mean that if you learn electromagnetic theory, you will know everything about chemistry. But everything we know about chemistry can be traced back to some electromagnetic effect. Chemical bonding is all about the electromagnetic forces between elementary particles. Chemistry deserves to be its own subject with its own ideas because the electromagnetic interactions get very complicated, and it’s very difficult to predict, based on electromagnetic ideas alone, how molecules are going to interact, react, and behave.
At a microscopic (some would say fundamental) level, sound is electromagnetic in nature. Sound is a pressure wave caused by the interaction of atoms or molecules in a gas, liquid, or solid. These atoms and molecules are interacting via electromagnetic forces.
Electricity holds atoms together! No electricity, no atoms. No atoms, no life. Electricity is fundamental.
EM theory is the prototypical example of a field theory, that is, a theory whose important quantities depend on space or spacetime. Modern theories of elementary particle physics are based on quantum field theories, the quantum versions of theories like electromagnetic theory. In fact, electromagnetic theory does not need to be modified to incorporate quantum ideas. The Maxwell equations are still the Maxwell equations in the quantum version of electromagnetic theory, but the mathematical objects like electric field and magnetic field are interpreted differently, as operators rather than numbers or vectors. The quantum version is quite a bit more complex, but it starts with the same Maxwell equations that we will study in this course in the classical version of the theory.
Einstein wrote about special relativity in 1905. Maxwell wrote his equations in 1865. Maxwell’s equations did not need to be modified at all with the advent of special relativity. They were already relativity-ready. The same cannot be said for the classical theories of mechanics, like Newtonian gravity, or even some versions of Newton’s second law.
It seems that electromagnetic theory was onto something fundamental about the universe.
Newtonian mechanics is incredibly useful, and beautiful, but it cannot be said to express our current best ideas about the universe. The 20th-century ideas of quantum mechanics and relativity have each led to newer theories that are slightly different from Newtonian mechanics, although they give essentially the same answers for slow massive things.
Electromagnetic theory, on the other hand, passed unchanged through the 20th-century quantum and relativity revolutions.
Light is an electromagnetic wave! Light is a wave of electric and magnetic fields. Electromagnetic theory is three theories in one. It’s been known since the early 1800s, when Oersted found an electric current can deflect a compass needle, that electricity and magnetism are related. By 1865, Maxwell understood that they belong as part of a single theory, and that the single theory interprets light as an electromagnetic phenomenon.
Here are four connections between electricity and magnetism.
Physicists enjoy when a small number of ideas are responsible for a vast array of phenomena. Maxwell’s reduction of electric, magnetic, and optical phenomena into a single theory seems like a great simplicity from a certain perspective. (However, the single theory is not simple from an ordinary human perspective. It’s only simple from a mathematical perspective. We might say the theory is profoundly simple from the perspective of sophisticated mathematics.)
It is expected that students will
The textbook for the course is Learn Physics with Functional Programming, by Scott N. Walck, No Starch Press (2023), ISBN 978-1-718-50166-9. This book contains numerical and computational techniques in electromagnetic theory. I will refer to this book as LPFP.
There are several ways to read a textbook.
I believe the textbook is worthy of close reading (not every book is), meaning that your learning improves by spending time with the book, that a slow reading is helpful, and that a second and third reading are likely to show you more than you got the first time.
While I believe the book worthy of close reading (I wouldn’t have assigned it as a required textbook if I didn’t), I don’t expect that you will always have the willingness or ability to read it closely. My job is to explain things to you, to help you read the book, to let you know when some things are more important than other things, to try to predict what will be difficult for you, and to try to convince you that this is one of the coolest subjects in the universe (which it just objectively is).
If one extreme is you doing a close reading of every reading assignment, another extreme would be me not asking you to do any reading and just explaining everything to you. If I was an entertaining figure, you might want this, but in any case we do not have the time for it. I cannot explain everything I want you to know and show you every skill I want you to have in 42 50-minute periods. So you need to do some learning on your own, some learning in class, and some learning in office hours or meeting with me. We might think of this as a three-legged stool of learning. We need all three parts.
Our goal then is to take a middle path between these two extremes. I will explain the things I think are most important and most difficult. The reading will help you understand a lot of things I don’t have time to explain, and you will ask questions about anything you are not understanding. You will decide how and when to skim, read closely, and reread based on you own assessment of how well you understand something and how well you need to understand it. I will do my best to set clear expectations of what I want you to know and what I want you to be able to do.
Why should we study how to get the computer to do electromagnetic theory? Computers weren’t around when EM theory was invented. EM theory has been taught for many decades without computer involvement. It’s going to take some effort to figure out how to use a computer in a helpful way. So why do it?
The traditional tools of algebra, calculus, and differential equations only get us so far. They can’t solve most problems. The theory tells you how to make (partial) differential equations, but you can’t solve them exactly. We don’t know how to write down functions that exactly satisfy the differential equations. Traditionally, you spend a lot of time studying situations that can be solved exactly, and then come up with tricks to approximate the other situations that can’t be solved exactly.
So, there are the exactly solvable problems, and then there are all the rest. We need methods that allow us to approximate the solutions to all these other problems.
There are some simple, standard approximations, that are known to be reasonably good, and don’t involve tricks. The problem is that they require an enormous number of exceedingly boring computations. And here is where the computer comes to the rescue. Just by being able and willing to do an enormous number of simple, boring computations, the computer can give us good, approximate solutions to many problems.
Why not use all the tools at our disposal, and in particular the computer, to help us solve our problems? Computers can do things that calculators can’t. I don’t predict the death of the pocket calculator, but who knows? The slide rule is, if not dead, an eclectic tool used by very few people.
Physics societies like the American Association of Physics Teachers (AAPT) have been encouraging physics teachers to include more computer techniques in their courses.
Just like mathematics is a valuable skill in itself. Knowing something about programming is useful for getting a job, but it’s also useful for organizing your thinking. Writing code is not just about getting the computer to do something. It’s also about expressing ideas in a formal language in a way that makes sense to people. And so, for the same reason that essay writing can help you clarify your ideas about art or politics, code writing can help you clarify your ideas about physics.
Haskell’s types and higher-order functions are particularly useful in helping us understand a theory.
So, it’s not just that we want to do all the ugly problems, or the real problems, or the practical problems. We do want to be able to do these, but using the computer can actually help us understand the theory itself. It can give us real insight.
An exam is an opportunity to demonstrate what you know about physics. There are three regular exams and one final exam in this course. The dates of these exams are listed later in the syllabus. Each exam consists of about three problems.
An exam is an individual endeavor in which you write and submit your ideas, your solutions, your guesses, and your work.
During an exam,
During an exam,
There will be portions of exams in which we will use a computer. During those portions, you may not use the computer to communicate with other people (exceptions: you can send me an email and use Canvas to submit your work), you may not search for help on the web or anywhere else, and you may not engage in any activity which violates the spirit of an exam being a one-person activity designed to probe what you know and what you can do. We will talk about the details closer to the first exam.
If you have any questions about whether a particular resource is allowed or not allowed during an exam, please ask me.
At the end of the semester, we will have a comprehensive final exam.
You should not think that office hours are only a time for people that need remedial help. Coming to office hours is helpful for people at all levels. Nobody is too advanced or too far behind to benefit from coming to office hours. A typical student in this class probably cannot get a high grade without coming to office hours, at least from time to time. Even if you don’t have specific questions, I can suggest problems for you to work on that will deepen your understanding, putting you in a better position for exams.
The homework is the centerpiece of this course. It is in doing the homework problems that you will begin to understand electromagnetic theory. Give the homework problems the time they deserve. I expect that many of the problems I am asking you to work will take about one hour each. I would not ask you to do these problems if I didn’t believe that the process was worth your time. You cannot succeed with this subject if you wait until the day before the homework is due to start. Start the homework a week before the due date by reading the problems and seeing if you can do any of them. Come to me with questions, or if you get stuck.
You may work together on the homework, talking about how to solve the problems, but you must write your homework solutions independently. Do not copy homework solutions from the web or from your classmates. Copying another person’s homework solutions is an act of cheating and plagiarism. Submitting your own work for the homework will cause you to learn electromagnetic theory. Everything that you write in your homework solutions you should be able to explain to me if I were to ask. This does not mean that your homework needs to be perfect, only that it must have come from your mind.
Sometimes people like to work together on a white board. This can be a good way to work, but it has a problem. The problem is that once people think they have the answer, everybody copies what’s on the white board. This is a problem, because does everybody really understand what’s on the white board? Maybe. Maybe not. Here is my suggestion if you want to work together on a white board. After you get to the place where you think the white board has the best answer, stare at it. Does it make sense to you? Could you remember it? Could you remember the rough steps? Then, don’t copy anything from the white board. Erase it. Try to reconstruct what was there on your own paper. Better yet, try to improve on what was there by writing it in a more organized way. Maybe it seems crazy to you to do this, but doesn’t it seem to be in the interest of learning? If multiple people copy from the same whiteboard, I will see the same thing on their submissions, and I don’t want to see that. If you give these problems some individual thought (which is a wonderful way to learn), even after you’ve talked with others about how to do it, you will not write the same thing that anyone else writes. There will be similarities, but it won’t be the same. So please do whatever you need to do to ensure that I don’t see the same thing on multiple submissions. Learning is hard. Cheating is easy. I know your time is limited. You have me a resource. Ask me for help instead of cheating.
If you can’t finish some of the problems before the due date, turn in what you have done. It is still worth trying to do the remaining problems, because they all have a purpose in learning electromagnetic theory. If you know in advance that you will have trouble finishing the homework by the deadline, come and talk to me.
A portion of your grade is determined by class participation. Obviously, attendance is a prerequisite for participation in class.
We will take turns being scribe for the class. When it is your turn to be scribe you write down the ideas that people in the class have for how to do a problem. You are not expected to do the problem on your own, but you can include your own ideas in what you write.
If you attend every class, and participate by scribing when it is your turn, you will have a perfect score for this area. If you need to miss a class, see me in advance and I’ll give you an alternative assignment.
Your grade will be determined by a weighted average as indicated in the table below.
| Exams | 45% |
| Homework | 30% |
| Class Participation | 10% |
| Final Exam (comprehensive) | 15% |
Your letter grade for the course is determined by the weighted average. The minimum weighted average (out of 100) required for each letter grade is indicated below.
| A | 93 |
| A- | 90 |
| B+ | 87 |
| B | 83 |
| B- | 80 |
| C+ | 77 |
| C | 73 |
| C- | 70 |
| D+ | 67 |
| D | 63 |
| D- | 60 |
| F | 0 |
Homework and exams can only be made up in the event of serious circumstances such as illness. There is no extra credit in this course.
| Date | Topic | Read before class |
|---|---|---|
| 08/25 | Welcome | |
| 08/27 | Vector Algebra | |
| 08/29 | Haskell Calculator | LPFP 1 |
| — | ||
| 09/01 | Functions | LPFP 2 |
| 09/03 | Types | LPFP 3 |
| 09/05 | Derivatives in Haskell | LPFP 4 |
| — | ||
| 09/08 | Vectors | LPFP 10 |
| 09/10 | Spherical Coordinates | LPFP 22, pp 421–426 |
| 09/12 | Cylindrical Coordinates | LPFP 22, pp 427–433 |
| — | ||
| 09/15 | Fields | LPFP 22, pp 433–446 |
| 09/17 | Gradient | |
| 09/19 | Continuous Charge | |
| — | ||
| 09/22 | Continuous Charge | |
| 09/24 | Exam 1 (Differential Vector Calculus) | |
| 09/26 | Curves | LPFP 23, pp 449–452 |
| — | ||
| 09/29 | Surfaces and Volumes | LPFP 23, pp 452–458 |
| 10/01 | Line, Surface, and Volume Integrals | |
| 10/03 | The Fundamental Theorem for Gradients | |
| — | ||
| 10/06 | No class (fall break) | |
| 10/08 | The Fundamental Theorem for Divergences | |
| 10/10 | The Fundamental Theorem for Curls | |
| — | ||
| 10/13 | Charge distributions | LPFP 24, pp 461–466 |
| 10/15 | Charge distributions | LPFP 24, pp 466–471 |
| 10/17 | Electric Field | LPFP 25, pp 473–483 |
| — | ||
| 10/20 | E from point charges | |
| 10/22 | Continuous distributions | LPFP 25, pp 483–494 |
| 10/24 | Continuous distributions | |
| — | ||
| 10/27 | Scalar integrals | LPFP 25, pp 494–502 |
| 10/29 | Exam 2 (Integral Vector Calculus and Coulomb’s Law) | |
| 10/31 | Gauss’s Law | |
| — | ||
| 11/03 | Applications of Gauss’s Law | |
| 11/05 | Electric potential | |
| 11/07 | Electric potential | |
| — | ||
| 11/10 | Electrostatic Energy | |
| 11/12 | Current distributions | LPFP 26 |
| 11/14 | Lorentz Force Law | |
| — | ||
| 11/17 | Continuity Equation | |
| 11/19 | Biot-Savart Law | LPFP 27 |
| 11/21 | Biot-Savart Law | |
| — | ||
| 11/24 | Exam 3 (Gauss’s Law, Biot-Savart Law) | |
| 11/26 | Reflection and digestion: What have we learned so far? | |
| 11/28 | No class (Thanksgiving break) | |
| — | ||
| 12/01 | Ampere’s Law | |
| 12/03 | Ampere’s Law | |
| 12/05 | Review | |
| — | ||
| 12/08 | Final Exam (Cumulative) | 8:30–11:00 am |
| Program Goal | Course Objective | Assessment |
| Graduates from our program will have a working understanding and knowledge of fundamental areas in physics. | interpret the force between charged particles in terms of electric and magnetic fields | Exams 2, 3, and Final Exam |
| apply Maxwell’s electromagnetic theory to specific physical situations | Final Exam | |
| calculate the electric field produced by a charge distribution | Exam 2 and Final Exam | |
| calculate the force on a charged particle moving in an electromagnetic field | Exam 3 and Final Exam | |
| explain the relationships between electricity and magnetism | Final Exam | |
| Graduates from our program will have a working understanding and knowledge of mathematics along with computational skills necessary for advanced work in physics/engineering. | describe physical situations using the mathematical language of scalar and vector fields | Exam 1 |
Any student who submits work that is in violation of the academic honesty policy will be subject to the penalties described in the College Catalog and outlined in LVC’s Academic Honesty Policy. Lebanon Valley College expects its students to uphold the principles of academic honesty. Violations of these principles will not be tolerated. Students shall neither hinder nor unfairly assist the efforts of other students to complete their work. All individual work that a student produces and submits as a course assignment must be the student’s own.
Cheating and plagiarism are violations of the academic honesty policy. Cheating is an act that deceives or defrauds. It includes, but is not limited to, looking at another’s exam or quiz, using unauthorized materials during an exam or quiz, providing unauthorized material or assistance to another student, colluding on assignments without the permission or knowledge of the instructor, and furnishing false information to receive special consideration, such as postponement of an exam, essay, quiz, or deadline of an oral presentation; and fabricating evidence, sources, or source material. Plagiarism is the act of submitting as one’s own the work (e.g., the words, ideas, images, compositions, or other intellectual property) of another without accurate attribution. Plagiarism can manifest itself in various ways: it can arise from sloppy, inaccurate note- taking; it can emerge as the incomplete or incompetent citation of resources; it can take the form of presenting passages or work prepared by another as one’s own, whether from an online, oral, or printed source. It may also take the form of re-using one’s own previously submitted work (such as a paper written for a different class) without the current instructor’s knowledge and permission.
A student is culpable for violations of the academic honesty policy, as outlined above, when caused by either academic negligence or academic dishonesty. An act of academic negligence is when a student engages in behaviors outlined above through irresponsible ignorance or carelessness. Acts of dishonesty involve the intent to deceive or mislead. Initially, the instructor will make the determination that a violation of the policy may have occurred.Students who take part in violations as described above are subject to a meeting with an Associate Provost, who has the authority to take further action, up to and including expulsion from the College.
Students should be aware that the work they submit must be their own. Professors may create assignments or activities that require or encourage the use of AI. If such use is not either required or allowed explicitly, then students must assume that the use of artificial intelligence is *not* acceptable in any given assignment. In this instance, unacknowledged uses of artificial intelligence in student work can be deemed violations of our academic honesty policy (see above). If this is unclear in any way, it is the student’s responsibility to ask the professor about appropriate uses of AI for the assignment.
Audio and/or video recordings of the class sessions may be made by the College and/or by students who have been authorized by the LVC Center for Accessibility Resources to record classes as an accommodation for a disability. By participating in the class, all students consent to be recorded for these purposes. Any other recordings of class sessions are not permitted. Students participating in online courses are asked to respect the privacy of those participating in the class by ensuring that class sessions cannot be overheard by those who are not enrolled in the course.
College-wide course policies concerning the following topics can be found at https://lvc4.sharepoint.com/sites/LVCSyllabusPolicies.
It is the student’s responsibility to review these policies.