How fast do electrons travel through a wire, and if they are slow, why does the light come on almost the...

In article <5a202m$fni@news2.i-2000.com>, frankmi@i-2000.com (Frank
Michaels) writes:

Tough to say exactly who wrote:
>>>Hmm. Disclaimer: I'm not a physicist. But don't most electrons travel
>>>at or near the speed of light anyway?
>
>>Uh, no, they don't.  When you speak, the sound of your voice travels
>>at "the speed of sound," around 600 mph, but that does not mean that
>>the air travelling out of your mouth goes 600 mph.  I forget what the
>>speed of electrons travelling through a wire is, but it's surprisingly
>>slow.

Good analogy!

>It's approximately 85% the speed of light, which is fast, but *is*
>surprisingly slow when compared to photons. At 85% the speed of light,
>electron mass does not appreciably increase due to relativity.

At .85 c, an electron's kinetic energy (via E=.5mv^2) equals
(approximately) .185 MeV.  This is definitely "appreciable" compared to
the rest energy of .511 MeV, so we're in relativistic territory at .85c.
However, electrons traveling in a wire travel at nowhere near this
velocity!  The approximate drift velocity is given by v=I/nqA where I is
the current in the wire, n is the number of free electrons per cm^3 in
the wire, q is the charge on an electron, and A is the cross sectional
area of the wire.  A typical copper wire might have a drift velocity of
only 10^-4 m/s!  This is less than a millionth of a millionth of the
speed of light!  (Another way to think of it--that's about one meter per
hour!)

Why then, if the electrons travel so slowly, do we see light the instant
(almost) we turn on a light switch?  By way of analogy, consider a pipe
already filled with water.  If we put a drop in one end, another drop
will have to be forced out the other end almost immediately, even though
it might take a very long time for an individual drop to make it
through.  The process is similar in many other areas of life, including
transmission of sound, as stated above.  I hope this sheds a bit of
light on the issue.  (By the way, I _am_ a physicist.  But that doesn't
mean I don't make mistakes!)

-- Stan Guthrie <gsg5501@msu.oscs.montana.edu>

[ Editor: two figures are rough.  The speed of sound in air at sea
  level is about 760 mph, not 600.  And 10^-4 m/s x 3600 s/hour = 0.36
  meter per hour, so "about one meter per hour" is a generous rounding;
  the comparison with light holds: 10^-4 / (3 x 10^8) = 3 x 10^-13. ]