Hi glidera,
Suppose you have a perfect conductor, and "push an electron into one
end". You would be able to observe the electrical effect at the other
end almost instantaneously, even though that electron has not
travelled to the other end of the conductor.
In the same way, an electric light comes on almost as soon as you
flick the switch, even though the electrons have not travelled along
the length of the wire from the switch to the light. Informally,
that's because the wire is already "chock full of electrons", so
pushing one in at the switch end will push another into the filament
of the lamp.
But the effect is not truly instantaneous. When you push an electron
into one end of the conductor, it "nudges" the next one with its
electric field, and so on all the way down the wire until the
electrons at the far end are "nudged" and we can detect the signal.
The electric field of each electron propagates at the speed of light,
but the inertial mass of the electrons will mean that the speed at
which the electric signal propagates will fall short of the speed of
light:
"For a very rough estimate I believe electricity (the field) travels
in the range of about 0.66 to 0.9 times the speed of light in a
conductor."
Ask a Scientist - Voltage and Efficiency
http://www.newton.dep.anl.gov/askasci/eng99/eng99174.htm
"Electrical signals in a copper wire travel at approximately 2/3 the
speed of light."
WildPackets ? Technical Compendium, Technology Engineering Networking
http://www.wildpackets.com/compendium/EN/EN-Propa.html
"Speed of electricity/radio on copper wire: 2.3 x 10^8 m/sec"
Metrics.pdf
http://nest.cs.uiowa.edu/22C178f00/pdf/metrics.pdf
Although for most purposes this appears "instantaneous" to us, there
are some situations where the non-instantaneous speed is noticeable.
One is the echo that we sometimes hear on a long-distance phone call,
caused by the time taken for the electric signal to travel through the
phone network and back again. Another is the resonance that can occur
on a nationwide electric grid where a reflected signal arrives back in
time to reinforce the next cycle.
Two further points: Firstly, the same effect is obtained if we "pull
an electron out of one end" of a conductor instead of "pushing it in".
Secondly, the individual electrons in a conductor move VERY slowly.
Here's a web page with some rough calculations (and discussion)
showing a speed of 8.4cm (3 inches) per hour for a 100 watt bulb
connected to typical lamp cord:
Speed of electricity flow (speed of current)
http://www.amasci.com/miscon/speed.html
Now, having assured you that the propagation speed of the electric
signal is very fast but still less than the speed of light (under all
circumstances, in a conducting wire) I will whet your appetite with
two pieces of recent research, one of which refers to a displacement
current moving faster than the speed of light, and one of which
(cautiously) refers to an electromagnetic signal moving faster than
the speed of light:
"We are developing a completely new type of solid-state light source,
the Polarisation Synchrotron; the machine is based on the
interchangability of displacement current and real current in
Maxwell?s Equations. However, because displacement current has no
inertial mass, it may be moved faster than the speed of light,
resulting in extraordinary emission properties which our source
exploits."
Current Research ? Quantum optoelectronics (scroll to last entry on page)
http://www.physics.ox.ac.uk/CM/QuanOpt.html
"A near-field analysis ... indicates that the fields generated ...
propagate superluminally in the nearfield of the source and reduce to
the speed of light as the waves propagate into the farfield ... It is
shown that relativity theory indicates that these superluminal signals
can be reflected off a moving frame causing the information to arrive
before the signal was transmitted (i.e. Backward in time). It is
unknown if these signals can be used to change the past."
Near-field Analysis of Superluminally Propagating Electromagnetic and
Gravitational Fields
http://arxiv.org/pdf/gr-qc/0304090
The math in these papers is beyond me, but it seems like fascinating stuff!
Please request clarification if this answer does not yet meet your needs.
Google Search Strategy:
"speed of electric current"
://www.google.com/search?hl=en&q=%22speed+of+electric+current%22
"speed of electric current" light
://www.google.com/search?q=%22speed+of+electric+current%22+light
"speed of electric" "speed of light"
://www.google.com/search?hl=en&lr=&q=%22speed+of+electric%22+%22speed+of+light%22
"propagation speed" "electricity" copper
://www.google.com/search?hl=en&lr=&q=%22propagation+speed%22+%22electricity%22+copper
Regards,
eiffel-ga |
Request for Answer Clarification by
glidera-ga
on
12 May 2004 11:15 PDT
I thank you for your thorough search, but one thing I must mention. We
observe a current almost instanenously, but not quite, under an
applied voltage. The example I was referring to was an isolated,
nearly infinitely-long wire NOT connected to any battery so electrons
do not feel any force so they do not move due to an applied
electrostatic field. What I was referring to was the fact that if the
wire is indeed perfect, there will exist a molecular orbital called
the Lowest Unoccupied Molecular Orbital (LUMO) extending through the
length of the wire such that the electronic wavefunction will be
delocalized over the entire wire, and the probability to find the
electron is the same everywhere along the wire so that I can observe
it indeed instantaneously at the other end infinitely far away from
the other end where the electron was initially "dropped". Once again,
I appreciate your input and your time.
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Clarification of Answer by
eiffel-ga
on
12 May 2004 13:27 PDT
My apologies, glidera, I did not see anything in your question to
suggest that you were seeking a quantum physics explanation - and
indeed I would not be able to give one. Having said that, I have a few
comments to add:
1. It's not clear to me how you can disregard electrostatic fields as
you "drop an electron into" one end of a conductor. Even though we're
not using a battery, won't we need to consider the electrostatic field
of the added electron as it approaches the wire?
2. Suppose the wave functions of electrons in the (perfect) conductor
are indeed delocalized over the whole length of the conductor. Won't
it then be the case that as the length of the conductor approaches
infinity the probability of finding our new electron at the other end
approaches zero? And with a near-infinite conductor, doesn't the
energy difference between the Highest Occupied Molecular Orbital and
Lowest Unoccupied Molecular Orbital become vanishingly small (because
we have so many molecular orbitals)? So how are we going to measure
this effect?
But your core point is that the effect of the new electron is not
confined to a point but is present in the wavefunction across the
entire extent of the conductor, and that is a fascinating point.
Regards,
eiffel-ga
|
Request for Answer Clarification by
glidera-ga
on
12 May 2004 13:41 PDT
Eiffel, you make excellent points, I've concluded that it was worth my
$5 to engage in this discussion, and once again I thank you for your
time. You are completely right, the situation I presented is entirely
artificial, and you would not indeed be able to ignore such
electrostatic effects when the electron approaches the wire, but then
again there is no such thing as a perfect wire either. :) As far as
the band gap is concerned, I could modify the question to ask just
about a long wire and not infinitely long, also I don't believe you
would necessarily need the HOMO-LUMO gap i.e. there are methods other
than spectroscopic ones such as scattering, etc. that I'm sure may be
used. Once again, this situation would never exist and I applaud your
rebuttle to my last point. Again I appreciate this discussion. (If you
have nothing better to do, we could potentially continue this
discussion - langaidin10@hotmail.com). Thank you and have a good day.
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