I’ve been kicking myself for being at home the last few days without my copy of the text I’m using this coming fall in Advanced Electricity and Magnetism. I’ve been saying “oh well, I’ll wait until Friday (when I go back to work) to continue thinking about the standards for my course.”

But, I’ve decided there might be some value to trying to write my standards without the book handy. What I’d really like is to engage with you, dear reader, about what the core concepts of E&M are. The book certainly walks me through things, and I’ve started to note the sections that aren’t core, but here’s my blind attempt at some standards for the course. I’ll finish up the official list in about a week and, of course, the students and I will further update them throughout the semester. If you don’t mind, add some comments below about the appropriateness/priority of these based on your memory of the course (Griffiths or the like is best, but I’ll take Jackson-based memories too!).

- Holistic: I can use the multivariable calculus fundamental theorems (Gauss’ law, Stokes law, etc)
- I can derive all the relationships among the electric field, the electric potential, and the charge density (this is one of Griffiths’ triangles).
- this one might have to be broken down a little
- I can calculate the field and potential for a complicated charge density distribution.
- I can prove that there’s no field inside a conductor.
- I can discuss the uniqueness proofs about a situation with a given potential distribution.
- I can discuss the solution to the Laplacian equation in 1 and 2 dimensions.
- I can discuss the foundations of, usefulness of, and ramifications of the separation of variables technique.
- I can discuss the foundations of, usefulness of, and ramifications of the method of images.
- I can use the method of images to find the field and potential for an interesting charge distribution.
- I can analytically and numerically solve an interesting 3D laplacian problem with cartesian symmetry.
- I can analytically and numerically solve an interesting 3D laplacian problem with spherical symmetry.
- I can discuss the foundations of, usefulness of, and ramifications of the multipole expansion technique.
- I can numerically calculate the various multipole terms for an interesting charge distribution.
- I can discuss the foundations of, usefulness of, and ramifications of linear dielectrics.
- I can derive the boundary conditions of E and B fields (this one is out of order, I think).
- I can calculate the field and potential for an interesting dielectric system.
- I can explain the relationships among the magnetic field, the vector potential, and the current density (Griffiths other triangle).
- I’m leaning heavily on skipping the vector potential since I don’t think it’s core to this semester’s material. It does help a lot with bound currents in ch 5, though.
- I can calculate the magnetic field for an interesting current distribution, using both direct integration and symmetry techniques.
- I can explain the microscopic origins of ferromagnetism, diamagnetism, and paramagnetism.
- Something about H vs B but not sure what to do here.
- I can write down and briefly explain Maxwell’s equations in materials
- not sure if this should be 3 (in material, out of material, with Maxwell’s and Faraday’s corrections)
- I can explain what emf is.
- I can explain what motional emf is
- I can explain why we need a third field that we also call the electric field.
- I can calculate the motional emf in an interesting situation.
- I can explain Maxwell’s corrections to (here I forget which one is corrected, but you know what I mean ;-)
- I can calculate the fields inside a charging capacitor.
- I can explain the origins of light.

Ok, I got a little too “I can explain . . . ” towards the end there, but it’s a passable list without having the book next to me. Again, I’d love to hear what you think. Here are some ways of thinking about it:

- What you actually remember doing in the class
- What you think a student should remember at the end of the class
- What you think a student should still remember 1 year after the class is over
- What a student needs to know to call themselves a physicist
- Other?

Grab the learning goals that Colorado faculty developed. Lots of other resources in there too: http://www.colorado.edu/physics/EducationIssues/cts/index.htm

(look for Junior Level Electricity and Magnetism)

I have modified their Quantum learning goals for my own use. They are very thorough.

I like their learning goals but they’re not specific enough. I think I’ll likely make use of their organization, though, instead of being a slave to chapter headings.

I just looked at the E&M ones and they are nowhere near as exhaustive as their junior quantum ones. For the junior quantum course, Steve Pollock had made a supplemental list of very specific things which are commonly asked on exams which would be very easy to turn into standards.

“Discuss” seems a tad vague for a standard. You don’t really just want them to discuss it; you want them to be able to reveal understanding of it, or its implications, or something. So say so.

Hi Ian,

I don’t like “discuss” either, but I’ve struggled with what to use when I don’t actually mean “derive.” “Reveal understanding” is what I mean, of course, but for some reason I think it sounds odd. I’ll put some thought into this over the next week before class starts and see what I can come up with.

The kind of standard that’s hard to put into SBG: “I can solve weirdo unusual problems and analyze weirdo unusual situations using the principles of E&M, even when they don’t follow the pattern of ‘normal’ problems I’ve seen.”

I feel like I had a lot of success with just this sort of thing in Theoretical Mechanics last year by using the word “interesting.” The class and I came to that word in our discussions and it ended up working pretty well. For E&M, I think there might be more mixing of the concepts, or at least the possibility of it for potential standards. There are a lot of really good problems in Griffiths that I hope to point to as good examples of “interesting.”. The problem is actually setting one of the problems as a standard because eventually I’ll likely show them how I would do it.

I like this sort of standard because it is the type of thing that a student who is able to earn a really high mark should be able to do to show mastery of the material.

Another favorite of mine: “I can find examples of real-world phenomena and technology that exemplify the various bits of physics we’ve learned about, and use the physics to qualitatively explain real-world phenomena.”

This one I like a lot. It’s much more defined than “interesting” while still being quite flexible. Thanks!

Hi Andy,

It has now been 15 years since I have seriously thought about E&M, but I will comment on the process: I love that you (at least, temporarily) ditched the textbook. I think the textbook might have too much influence, causing us to forget about important topics it omits and suggesting that other topics are more important than they are.

It will be interesting to hear how close these end up being to your actual standards.

Bret

Ok, now I’m looking at my margin notes in the book. Here are some more potential standards topics:

Chapter 1:

- divergence of , dirac delta function

- Helmholtz theorem (theory of vector fields)

Chapter 2:

- calculate force on one charge based on a bunch of others (Griffiths “clock face” problem)

- energy of continuous charge distribution

- conductor with cavity problem

Chapter 5:

- show mag forces do no work (I really like how Griffiths covers this)

- multipole expansion for magnetization (note, needs vector potential)

Chapter 6:

- torque and force on magnetic dipole

- explain bound currents (easiest with vector potential)

- Compare and contrast D versus H

Chapter 7:

- field in a cylindrical wire (uniqueness application)

- inductance

- energy in mag fields (combine with electrical one?)

That’s not too long, I guess. Thoughts?

I have a suggestion for breaking down 2. I think you need a standard like, “I can identify and discuss the physical meaning of r vector, r’ vector, and r-r’ vector, discuss their relevance for finding E-field and potential, and explicitly show what’s happening to r, r’, and r-r’ when performing the integrals involved in finding fields and potentials.”

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