I find the textbook derivations of blackbody radiation mostly obtuse, too rooted in esoteric historical baggage, and unnecessarily difficult. All this annoyed me enough to come up with some notes on radiation that will make up the bulk of the next three lectures. The notes are not quite complete yet (close, probably 'done' by Thursday), and there are a few extra bits included beyond what we'll probably cover in class.
So, 1) don't be scared by the length of the notes, you're not responsible for all of it, 2) they are long because I purposely tried to only use PH105-106 material and relativity, 3) the gain in clarity will be worth the extra time in the end, and 4) I will spell out what material you are responsible for knowing on the exam, and it will mostly be what is in the textbook. The extra derivations are mostly just for clarity, you'll be responsible for the end result.
Anyway, here's the basic plan for the next few lectures.
We know from PH106 that accelerating charges emit electromagnetic radiation, i.e., light. We want to figure out how accelerating charges emit radiation in general, and specifically find the spectrum of radiation emitted from a hot object. Why should hot objects emit radiation? In short, individual charges in atoms acquire random thermal energy, which causes them to oscillate, which means they are accelerating, which means they radiate. We aim to calculate the spectrum of radiation emitted, within a simple toy model:
- Figure out how E and B transform when you change reference frames.
- Figure out the field from moving charges, particularly those that undergo acceleration.
- Find the radiation emitted from accelerating charges, particularly for simple harmonic motion.
- From the power corresponding to this radiation of energy, and find the radiation reaction force that must be present
- Use this force to compute the equation of motion and energy of oscillating, radiating charges.
- Model a hot object as a collection of charges randomly oscillating due to their random thermal energy.
- Realize the result is silly, and resort to Planck’s quantum hypothesis . . .
If that doesn't convince you, by deriving things now in the most general way possible, we'll get to re-use all this hard work later in the semester. Hopefully, by the time we are done with the semester, everything will tie together nicely ...