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I understand the basic statement of Poynting theorem of conservation of energy relative to electromagnetic field.

However, I fail to apply it to an example. Consider this classical case:

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Conservation of energy can be applied easily via Lorentz & Maxwell's equations(Faraday & Lenz & Ampere).

How can Poynting's theorem be applied? Or is it only applied relative to travelling waves?

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    $\begingroup$ Poynting's theorem can be applied to things other than traveling waves, e.g., it works just fine for capacitors. The problem with your example is that the only thing that "sees" an electric field is the sliding metal bar. The end result, if memory serves me, is something more akin to Ohm's law than Poynting's theorem (though one can be derived from the other). $\endgroup$
    – honeste_vivere
    Commented Nov 15, 2017 at 17:38
  • $\begingroup$ Related and duplicate if cell replace by moving conductor. What is the physical explanation for energy transport in simple electrical circuits? $\endgroup$
    – Farcher
    Commented Oct 25, 2021 at 7:54

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