Tuesday, August 26, 2008

Transversality of Electromagnetic Waves in the Calculus-Based Introductory Physics Course

First of all, let's get this out of the way. I love, love, LOVE, this type of articles. I like it when someone makes an effort to go over things that we learn as part of our basic physics education at the undergraduate level, and explains things in painful detail of things that either were not covered, or were not explained in great detail. In fact, some of these things can be quite puzzling at that time because of such deficiencies, and only later on, if we're lucky, do we finally understand why some of them are as described.

This preprint appearing on arXiv today, tries do to just that. The author had meticulously explained and derived why EM wave have transversed electric and magnetic components, something that isn't covered in great details at the introductory level. I like the fact that he used both physical arguments (observation from polarization) and rigorous mathematical proof based on Maxwell equations.

This is along the same spirit as the Marcella's paper "Quantum Interference with Slits" that I highlighted recently. In Marcella's paper, he painfully derived all the wave-like behavior one observes in single, double, and multiple slits without invoking any wave formalism at all, just purely quantum mechanical. It shows how QM can derive such a thing, something we all know it could, but never actually sat down and did it.

The other paper that I wish to highlight here is an old paper (if you call 1984 old) that explains something that just did not appear right when it is used in many standard intermediate E&M textbooks. The paper is titled "Force on a Dielectric Slab Inserted into a Parallel-Plate Capacitor" by S. Margulies (Am. J. Phys. v.52, p.515 (1984)). Here, he tackled on a confusing description of the origin of the force acting on a piece of dielectric slab that is partially inserted into a parallel-plate capacitor.

For example, how can the force act to pull the slab into the volume between the plates when the electric field there is perpendicular to this direction? If this is explained - the force is, of course, due to the fringe field - an apparent paradox arises: How can the virtual-work calculation yield an answer when it is explicitly based on the assumption of a uniform electric field existing only in the region between the plates, and so does not include the fringe field at all?

He then gave a very detailed derivation on this force that eventually matches what we get in standard textbooks, and in the process, explained the origin of this force based on the fringe fields that were neglected in the first place. It's a Tour de Force paper on details, details, details.

Does anyone have any similar papers that deal with the same type of revelations? I'd love to collect more of these.


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