In a cavity, the standing wave will constructively interfere with itself, so its energy gets higher while the oscillator is still vibrating. Since the vibration time is not a constant value, and sometimes the wall of the cavity absorbs some of the wave energy, the energy of a standing EM wave is probabilistic and follows Maxwell-Boltzmann distribution. Am I correct in the statement above?
Actually I'm thinking about the black-body radiation. To calculate the energy density in a cavity which is heated up to $T$, we assume that the cavity is a cube, and only standing wave can exist in it(Why?). First we need to calculate how many kinds of standing waves(how many different wave vectors) for one frequency $f$. This can be done with some mathematical tricks. And then we have to determine the energy of each wave $\overline{E(f)}$. And my question is, actually, why does this overline come from? Why is it an average energy, instead of a constant value?
Best Answer
Conservation of energy follows directly from Maxwell's equations, so if you convince yourself that energy isn't conserved when EM waves interfere, you've made a mistake, and you need to go back and figure out what your mistake was.
Not true. If you work out the right-hand relationships for two EM plane waves traveling in opposite directions, you'll find that if the E fields are in phase, the B fields have opposite phases, and vice versa.