SPEED OF "ELECTRICITY"
= cm/sec = ________I_______ Q * e * R^2 * pi = .0023 cm/sec or 8.4 cm/hour [ This is for 1.0A in #12 copper wire. ] [ Higher currents give faster drift, ] [ and thinner wire gives faster drift. ]This is for DC. Chris R. points out that for a particular value of frequency of AC, the "skin effect" can cause the flow of charges at the center of a wire to be reduced while the current on the surface becomes stronger. There then are fewer charges flowing overall, and hence the ones near the surface must flow faster. ("Skin Effect" is stronger at high frequencies and with thick wires. The effect can USUALLY be ignored in thin wires at 60Hz power-line frequencies.)
The size of the wiggleAnd about AC... how far do the electrons move as they vibrate back and forth? Well, we know that a one-amp current in 1mm wire is moving at 8.4cm per hour, so in one second it moves:
8.4cm / 3600sec = .00233 cm/secAnd in 1/60 of a second it will travel back and forth by
= .00233cm/sec * (1/60) = .0000389cm or around .00002 in.This simple calculation is for a square wave. For a sine wave we'd integrate the velocity to determine the width of electron travel.
So for a typical AC current in a typical lamp cord, the electrons don't
actually "flow," instead they vibrate back and forth by about a
hundred-thousandth of an inch.
The width of one CoulombOn thinking along these lines I notice something interesting: in copper, one coulomb of movable electrons has a certain size! There are about 14,000 coulombs of free electrons per cubic centimeter of copper.
= 8.5*10+22 elect/cc * 1.6*10-19 coul/elect = 13600 Coul./ccTherefore one coulomb would form a cube approximately 0.4mm across...
1/(13600cc^(1/3)) = 0.042 cmHA! A coulomb in copper is about the size of a grain of sand! We can now discuss electric currents within wires as if they were cc-per-second fluid-flows inside of small hoses. If an Ampere is one coulomb per second, we're REALLY saying that an Ampere is "one saltgrain-sized blob, moving each second, squeezing itself into whatever sized wire." So, for the usual sizes of wires used in electric circuitry, if we deliver one salt-grain per second (one amp,) that's a very slow flow. The tiny saltgrains are going by: bip, bip, bip, once per second.. In 16-gauge wire the saltgrain blobs would be morphed to fill the cross-section, so they would resemble very thin stacked pancakes. In 30-gauge wire the saltgrains would be almost undistorted, and so the charges would move at about 0.4 mm/sec during a 1-amp current.
Visible motion of chargesHere's another way to look at it. During electroplating, for each metal ion deposited on the metal surface, one or more electrons must move up to the surface to produce the electrically neutral metal. The layer of metal is slowly growing, while electrons and ions flow in towards that growing surface. Ah, but look closely: if each incoming atom needs one electron, then as the metal atoms stack up, the electrons must flow at a particular speed. This speed is exactly twice as fast as the growing electroplated metal! In other words, if we're electroplating just the tip of a metal wire (making the wire grow slowly longer,) then the flowing charges in that wire are moving very slowly: twice as fast as the advancing wave of newly plated metal. Pretty cool, eh?
One thing's not certain in the above calculations: the charge density for copper. My above value for Q assumes that each copper atom donates a single movable electron. The email from the person below points out that this might not be true. For example, if only one in ten conduction electrons are movable, while the rest are "compensated" and frozen, then the speed of the charge flow will be ten times greater than 8.4cm/hour.
One final point. Electrons in metals do not hold still. They wiggle
around constantly even when there is zero electric current. However, this
movement is not really a flow, it is more like a vibration, or like a
high-speed wandering movement. How should we picture this? Well,
remember that we can speak of wind or of flowing water as if they had
a genuine velocity... yet a similar type of rapid wandering motion is
found in the atoms of all normal liquids and gases. Even when the wind is
less than one MPH, the air molecules are zooming around at hundreds of
MPH. Even in still air the molecules still wiggle
around at the same high speeds. We usually ignore this when discussing
the motions of air, and instead take the average velocity of all molecules
in a certain
small volume. We call it "thermal vibration," and we see the fast
movements as a separate issue. Therefore we should do the same with
circuitry: the electric current is akin to wind, while the high speed
wandering motions of individual electrons is akin to thermal vibrations of
individual air molecules. In the above article I concentrate on the slow
which is measured by electric current meters, and I ignore the electrons'
high speed "thermal vibration."
I've seen one way to directly observe and measure the drift velocity of charges in a (non-metal) conductor. Connect metal electrodes to the ends of a large salt crystal (NaCl), then heat it to 700 degrees C and apply high voltage to the electrodes. At this temperature the salt becomes conductive, but as electrons flow through it they discolor the crystal, and a wave of darkness moves across the clear crystal. The velocity of this slow-moving wave can be measured. (And if you double the current, the speed of the wave doubles.) This demonstration appears in:
Physics Demonstration Experiments (two volumes)
Date: Tue, 17 Oct 95 09:53:00 PDT
From: O. Quist
Subject: Re: your mail
On Fri. 13 Oct 1995 Bill Beaty Wrote:
> Very interesting! All the sources I've encountered state that
> each atom in a conductor contributes one (or two?) electrons to
> the conduction band. Might you know a rough figure for the
> actual number of electrons/atom in a copper lattice? How much
> smaller is it than 1.0?
The number of electrons in the conduction band is indeed as you say. But,
that is not what I was saying (below). The actual number of electrons
which contribute to the electrical current is not equal to the number of
electrons in the conduction band.
The electrons which contribute to electrical conduction are those
electrons within the Fermi Surface which are "uncompensated." From
symmetry, these electrons lie on, or near the surface, and result as the
Fermi Surface is "shifted" by the electric field. The fraction of
electrons that remain uncompensated is approximately given by the ratio
(drift velocity)/(Fermi velocity). The result is the number of electrons
which produce an observed current being considerably less than Avagadro's
The number of electrons producing current being thus reduced, produces an increase in their average velocity. Average electron velocities are more probably in the meters/sec range rather than the 10ths of a millimeter/sec as is predicted by the free-electron theory.
Date: Tue, 16 Jun 1998 00:31:01 -0500
From: Roy M.
To: William Beaty <>
Subject: Re: Electron drift velocity in metals
Its a minor point, but, drift velocity is an average. If some of those
conduction electrons are "stuck", they still contribute to the average.
If you want to exclude the slowest 99% then the average of those you do
allow will be higher. But, its probably an unnecessary refinement in
this context, which is to treat electrons like classical particles and
calculate average drift velocities.
Anyway, the effect of which you refer involves the fermi theory, Pauli
exclusion and conservation of energy. In effect fewer electrons
participate in conduction, but their mean free path is longer.
The explanation is something like: no more than two (with opposite spins)
electrons can occupy a given state. When two electrons collide, their
final states must have the same total energy and the final states must
have been vacant. Thus, if all the states which can be reached at a
given energy level are already filled, then the two electrons cannot
collide. Net result is that electrons in low energy states are "stuck"
in those states. So only the relatively few electrons in high energy
states are really available to participate, but most of the other
electrons are not available to collide with the high energy electrons so
that those electrons that do participate go futher (mean free path) than
you might expect.
Subject: Re: Electron drift velocity in metals
Organization: Eskimo North (206) For-Ever
Interesting. If part of the conduction band is excluded from conducting, then the average drift velocity of all of the conduction band electrons is unaffected.
However, the average drift velocity of the "non-stuck" electrons becomes
much greater. The "stuck" electrons are not "conducting" and are not
part of the drifting population, even though they are in the conduction
After all, for purposes of calculating the drift velocity we could have
counted all the valence electrons in every copper atom too (since they are
all "stuck") and then claimed that the average drift velocity for
electrons was even slower than if each atom contributed only one electron
to the current.
I wonder what the real percentage of "free" electrons might be. If it was
tiny, then perhaps the drift velocity is in fact very large. If it was
REALLY tiny, then perhaps the velocity of the non-stuck electrons rivals
the thermal/quantum random motion speeds, and therefor electric current is
not a tiny average motion of a fast-moving random cloud.
Wouldn't it be interesting if electric currents in metals tended to create a few relativistic electrons, rather than a large number of slightly drifting "trajectories."