Three question E&M I final today, roughly as follows.
1a. As a starting point, calculate the electric potential on the axis of a ring (radius a) of uniform charge. (trivial)
1b. Use the expansion in Legendre polynomials to do an off-axis extrapolation of 1a to find the potential everywhere. (Conceptually not bad, mathematically tedious)
1c. Roughly speaking, examine the continuity of the r < a and a < r solutions at r = 1. (not difficult assuming you have 1b right)
2. Hollow dielectric sphere in a uniform electric field. Find the potential everywhere. (Average conceptual difficulty, very mathematically tedious)
3. Sort of a long story, but basically writing vector potentials in the Coulomb gauge and extracting certain information about the resulting fields.
How'd I do on the exam? Not perfect, but not so bad. B at least, fingers crossed on the A. Statistical mechanics is next Wednesday, and that's going to be a horror show. There is just so much stuff, and it's all hard. Oh well. Lots of studying to do.
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Is this Jackson E&M? Seems a little light on the Green's functions.
Yes, it's Jackson. But don't worry, we did Green's functions to death on the midterms and the homework.
Green's functions are so neat.
I have really bad memories of my grad level stat mech class. The professor was very good in class (kind of a jerk outside of it), the lectures were fascinating, but the exams just wiped the floor with me.
This is the depressing part about physics grad school. I took that class two years ago, got an A- in it, and by all indications I should have a PhD in a couple of years unless something goes horribly wrong. But those questions sound challenging now that I haven't thought about E&M in a while. I certainly couldn't do them without the book.
Like Walter Rudin's "Principles of Mathematical Analysis", Jackson's "Electrodynamics" seems to be one of those books that is lauded _because_ it is deliberately difficult, even obtusely so.
Reading jeffk's comment, and in light of the many complaints made about this book, I question the wisdom of asking students to spend a semester expanding in terms of Legendre polynomials or some such like.
While some problems in the book are worthwhile, the majority are rather pointless exertions. I think EM courses would be a lot more worthwhile without them. Toil, in and of itself, does not signify progress.
OMF, I can see your point on that, but I was more generally just bitching and I don't think I advocate not having the class. The thing about physics is it's a somewhat (but not completely) arbitrary collection of science bound together partly by related concepts but also partly by historical tradition. It's fairly broad, and it's also very HARD. The inevitable result of this is you'll suffer through things that you'll forget, but on some deeper level help you understand the way it all ties together. I'm ok with it, but Matt should be warned now he's as good at E&M as he's ever going to get unless he goes into space physics.
It's tempting to think as you proceed in your education you get more and more knowledgeable, but your ability to solve some problems diminishes as you move past the early grad phase, particularly for experimentalists.
"It's tempting to think as you proceed in your education you get more and more knowledgeable, but your ability to solve some problems diminishes as you move past the early grad phase, particularly for experimentalists."
http://www.phdcomics.com/comics.php?f=1056
OMF makes an excellent point @6, to which I would add "by hand". Expanding functions is a common tool in mathematical physics, and E+M is where you really learn how to project one function onto a basis made up of a family of orthogonal functions.
I think your question 2 was on one of my grad E+M exams! I'd say it is conceptually easy (see page 329 of Purcell's "freshman" Berkeley physics text). The field of the polarized sphere is what is challenging about it.
Jeff's point assumes that you learn the concepts in between all of the math. I'm not sure this is always the case. I learned more physics from Purcell, which is, by the way, the perfect companion to Jackson's math.