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[Phys-l] Poynting Vector

Consider a charged simple parallel plate capacitor in a static uniform
downward-directed magnetic field. The capacitor is oriented so that
from our point of view, the electric field between the plates of the
capacitor is directed rightward. Poynting tells us that between the
plates, energy is flowing away from us at a rate proportional to EB.
Where is that energy coming from and going to?