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Poynting field outside a resistor

On Thu, 18 Jan 2001, Leigh Palmer wrote:
That is a "correct" explanation which reifies the "flow
of energy", renaming it "the Poynting flux". It is, as I
pointed out, a physically useful way to consider the
problem, but don't get carried away. In a simple resistor
carrying a current the Poynting flux which accounts for
the Joule heating effect comes in radially from infinity.

From infinity? But what about the Poynting field which connects the power
supply to the resistor?

Draw some lines of "Poynting flux" for a simple circuit which includes a
battery and a resistor. This "flux" will look roughly like a dipole
field, with the battery being the "source" and the resistor being the
"sink." The lines of "Poynting flux" which dive into the surface of the
resistor all originate on the electrolyte/electrode interfaces within the
battery.

Here's a very crude hand-drawn version:

http://www.amasci.com/elect/poynt/fig8.gif

In this diagram the black square is the metal circuit, with the battery at
the left and the resistor at the right. Only a line of "Poynting flux"
which leaves the battery and extends to infinity... would return from
infinity and dive into the resistor.

Sure, the numbers work out fine, but do you believe that
God in her infinite omniscience, was also sufficiently
prescient that she started this energy flowing coherently
inward toward the resistor at some time in the distant
past - from all sides!?

If an empty copper/zinc battery jar was suddenly filled with electrolyte,
then the lines of Poynting flux would propagate towards the resistor as
the transient waves in the EM fields moved forward.

Let's make a distinction between how we calculate and how
we explain. They are two different things.

Not in this situation though.


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