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Yep! I recently found yet another way to express this. If we could move
electrons at a few cm per second, the wire would heat up a rate of
kilowatts per cubic mm, it would glow white hot and melt, if not vaporize.
Or conversely, if we could grab the electron-stuff of a wire and shove it
along, it would take kilo-newtons force to make it move at cm per second
rate (and of course it would smoke and melt.) The "electric fluid" within
wires is not like water. It behaves more like cold tar being pumped
through a sponge! Amazing that electrical devices work at all.
I think that there *might* be a misconception afoot here. It is *not* true
that the conduction electrons in a current-carrying wire move at speeds
anywhere near the mm/s order of magnitude.
Because of the large mean free path length and mostly single independent
particle-like nature of electron conduction, the image of tar as an analogous
fluid may be somewhat misleading. But, because the responding fluid very
quickly reaches its terminal velocity due to interactions (i.e. collisions)
with defects, impurities and phonons, the picture of any friction-dominated
fluid such as cold tar flowing through a sponge *does* have something
going for it.
My picture is one of air flowing through a porous open-spongy
or fluffy insulating material such as attic insulation. In this case the
typical speeds of the molecules in the air are orders of magnitude faster
than the wind speed of the light breeze flowing through the fluffy medium.
This picture also has its faults, as well. Because electrons are *much* less
massive than the molecules of the gases found in air, their speeds would be
much faster, at a given temperature, than the speeds of the air molecules--
even if they (the electrons) were not, additionally, effectively sped up much
further (and reduced in concentration) by the indirect effects of the Fermi-
Dirac statistics.