Interpretation - wykład - Gauss' theorem

Interpretation Now the first term represents the rate of increase of stored energy per unit volume. The
second term represents the rate of working per unit volume of the field on the conduction
currents J. These currents might result in the dissipation of energy in the resistance of
the medium, or might, if flowing in a pair of external terminals, result in the supply of
electric power to or removal of electric power from the field system. The third term must,
by conservation of energy, represent the rate of flow of energy per unit volume out of the
volume by electromagnetic means. In fact the energy flows out in the form of photons, but
we are not working to a microscopic scale, so quantization of the field and such conditions
do not concern us. To us it looks as if energy is being continuously transported by the
field in an amount div (E × H) per unit volume, per unit time.
Now by Gauss' theorem
I
S
(E ×H) · ds =
Z
v
div (E ×H) dv. (7.13)
So we identify E×H as the power flow per unit area
across any surface.
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