In several recent threads the Poynting's theorem was brought up, and the discussion there became a distraction from the questions at hand without really being solved: https://www.physicsforums.com/showthread.php?t=621018 (starting #74) https://www.physicsforums.com/showthread.php?t=628896 (this post continues from the discussion starting with post #198) Roughly, the theorem states (I think) that the energy that dissipates as heat inside a volume equals the energy that enters it minus the stored energy that is extracted from it. A basic issue is the meaning there of the term E.j. According to some, the energy transferred from EM fields to matter (work) is E.j. However, the texts that I consulted specify that it is the Ohmic heating rate, or the dissipated energy inside the volume under consideration. Clearly there is some ambiguity here. A paper that appeared a few years ago in Europhysics Letters 81 (6): 67005 (thanks Wikipedia!) - http://arxiv.org/abs/0710.0515 could be helpful. Clarifications are welcome!