SPEED OF "ELECTRICITY"
How fast does electricity flow? Well, it depends on what you mean by
"electricity." The word Electricity has more than one contradictory
meaning, so before we can talk about its flow, we have to decide on
which of several "electricities" we really mean. For a discussion
of electric current, see below. But for articles about fast-flowing
electromagnetic energy, see the
energy article, or an
OK, then how about this. When we turn on a flashlight, something called
an "electric current" begins to happen. Inside the flashlight bulb, the
thin filament-wire gets hot because there is electric current in the metal.
This current is a motion of something. How fast does this "something"
move? This question can be answered.
The quick answer
Inside the wires, the "something" moves very, very slowly, almost as
slowly as the minute hand on a clock. Electric current is like slowly
flowing water inside a hose. Very slow, so perhaps a flow of
syrup. Even maple syrup moves too fast, so that's not a good analogy.
Electric charges typically flow as slowly as a river of warm putty. And
circuits, the moving charges don't move forward at all, instead they sit
in one place and vibrates. Energy can only flow fast in an electric
circuit because metals are already filled with this "putty." If you push on one
end of a column of putty, the far end moves almost instantly. Energy
flows fast, yet an electric current is a very slow flow.
The complicated answer
Within all metals there is a substance which can move. This stuff has
several different names: the Sea of Charge, or the Electron Sea, or the
Electron Gas, or "charge." We often call it "electricity," and state
that electric currents are flows of electricity. Calling it
"electricity" can be misleading because many people believe that
electricity is a form of energy, yet charge is not energy, and currents
are not flows of energy. Also it can be misleading because the Sea of
exists within in all metal objects, all the time, even when the metal
hasn't been made into a wire and is not part of an electric device. If the
Electron Sea is "electricity," then we must say that all metals are
always full of electricity, and that batteries are simply
electricity-pumps. Better to call it by the name "charge-sea," and avoid
the misleading word "electricity" entirely.
During an electric current, the metal wire stays still and the sea of
charge flows along through it. When the flashlight switch is turned off
and the lightbulb goes dark, the charge-sea stops moving forward. Even
though it stops moving, the charge-sea is still inside of that wire. If
the flashlight is again turned on and two light bulbs are connected in
parallel instead of one, the electric current will have twice
as large a
value, and twice as much light will be created. And most important, the
charge-sea withing the battery's wires will flow twice as fast. In other
words, the speed of the charges is proportional to the value of
electric current; small current means low-speed charge-flow, large
high speed. Zero current means the charges have stopped in place. Note
that an electric current does not have just one speed within any circuit.
Charges speed up whenever they flow into a thinner wire. The high current
in a large flash-lantern's lightbulb will be much faster than the same
current in the other conductors in the lantern. Even though an electric
current is a very slow flow of charges, we can't know the actual speed of
flow unless first we know the *value* (the amperes) of the current in the
If a thin wire is connected in a circuit end to end with a thick wire, it
turns out that the charges in the thin wire move faster. This makes
sense: it works just like water in rivers. If a huge wide river moves
into a narrow channel, the water speeds up. When the channel opens out
again downstream, the river slows down again. The electric current in a
wire will be tend to be fast, even if the value of current is fairly low.
This means that we can't know the speed of the flowing charge-sea unless
we know how thick the wires are.
If a copper wire is connected into a series circuit with an aluminum wire
of the same diameter, the charges in the copper will flow slower. This
occurs because there is one movable charge per each atom in the metals,
but there are more atoms packed into the copper than into the aluminum, so
there is more charge in each bit of copper. When the charge-sea flows
into the copper, it gets packed together and slows down. When it flows
out into the aluminum, it spreads out a bit and speeds up. This means
that we cannot know how fast the charges flow unless we know how dense the
charge-sea is within the metal.
The speed of electric current
Since nothing visibly moves when the charge-sea flows, we cannot measure
the speed of its flow by eye. Instead we do it by making some
assumptions and doing a calculation. Let's say we have an electric
current in normal lamp cord connected to bright light bulb. The electric
current works out to be a flow of approximatly 3 inches per hour. Very
Here's how I worked out that value. I know:
- Bulb power: about 100 watts, about 100V at 1A
- Value for electric current: I = 1 ampere
- Wire diameter: D = 2/10 cm, radius R=.1cm
- Mobile electrons per cc (for copper, if 1 per atom): Q = 8.5*10^+22
- Charge per electron: e = 1.6*10^-19
cm/sec = ________I_______ = .0023 cm/sec = 8.4 cm/hour
Q * e * R^2 * pi
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 are fewer charges flowing overall, and hence they 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
The size of the wiggle
And 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 per second
And in 1/60 of a second it will travel back and forth by
.00233cm/sec * (1/60) = .0000389cm, or around .00002"
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 Coulomb
On 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./cc
Therefore one coulomb would form a cube approximately 0.4mm across...
1/(13600cc^(1/3)) = 0.042 cm
HA! 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
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 charges
Here'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
for copper. My above value for Q assumes that each copper atom
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
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)
H. F. Meiners, ed. Ronald Press Co 1970
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
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