What would Poynting vector mean physically if there is plane-parallel electric and magnetic field perpendicular to each other, like what we do in Hall Effect experiment? Or, in general, what would it mean in any static field configurations?
I always assumed that Poynting vector represent flux of photons that play their role in electromagnetic interaction. Like how any charge bend towards the direction the Poynting vector is pointing at (pun intended), regardless of their charge signs. It is like as if photons (or anything that conducts electromagnetic force) "hit" those electrons with given direction.
But this is problematic in many ways. First, I am not sure if such interactions, or, scattering can happen. I study astrophysics, and at that field, usually photon-electron cross-section is incredibly small. I need to do some calculations, but quite sure that photon scattering is not enough to represent what we observe in the lab.
Another and more serious problem is that, if Poynting vector really represents just photon flux, then those photons are from, where physically? Or, in that sense, where (physical-spatially) should "electromagnetic waves" are generated? We usually set up Hall Effect experiment with static E and B field, so what would be the frequency of photons?
So I am kinda confused. I also read an answer posted here that interprets Poynting vector as photons, but now I doubt this kind of interpretation. How much am I wrong? What would be a good way to interpret Poynting vector in static EM fields?
