Your Freshman electromagnetism question reminded me of a "mind opening" thought experiment where you envision a single electron floating in space. If you are stationary with respect to it, you see ONLY it's electric field. If you move with respect to it, you see a magnetic field. An oscillating motion results in EM radiation(photons).
If you get into it deeper 4d-Maxwell it turns out that electromagnitism is actually some sort of 4-dimensional stuff, and we see either electric field or magnetic field depending on our spatial relationship. Feynman had some great 4 dimensional solution which showed all this by emcompassing all of Maxwell's equations into a simple 4-d operator equation. Whenever I want to "space out" until I drool, I meditate on the 4-dimensional nature of EM.
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