What is the speed of electricity ?
The speed of electricity really depends on what you mean by the word
"electricity". This word is very general and basically means, "all
things relating to electric charge". I will assume we are referring to a
current of electrical charge traveling through a metal wire, such as
through the power cord of a lamp. In the case of electrical currents
traveling through metal wires, there are three different velocities
present, all of them physically meaningful:
- The individual electron velocity
- The electron drift velocity
- The signal velocity
In order to understand each of these speeds and why they are all
different and yet physically meaningful, we need to understand the
basics of electric currents. Electric currents in metal wires are formed
by free electrons that are moving. In the context of typical electric
currents in metal wires, free electrons can be thought of as little
balls bouncing around in the grid of fixed, heavy atoms that make up the
metal wire. Electrons are really quantum entities, but the more
accurate quantum picture is not necessary in this explanation. (When you
add in quantum effects, the individual electron velocity becomes the
"Fermi velocity".) The non-free electrons, or valence electrons, are
bound too tightly to atoms to contribute to the electric current and so
can be ignored in this picture. Each free electron in the metal wire is
constantly flying in a straight line under its own momentum, colliding
with an atom, changing direction because of the collision, and
continuing on in a straight line again until the next collision. If a
metal wire is left to itself, the free electrons inside constantly fly
about and collide into atoms in a random fashion. Macroscopically, we
call the random motion of small particles "heat". The actual speed of an
individual electron is the amount of nanometers per second that an
electron travels while going in a straight line between collisions. A
wire left to itself carries no electric signal, so the individual
electron velocity of the randomly moving electrons is just a description
of the heat in the wire and not the electric current.
Now, if you connect the wire to a battery, you have applied an
external electric field to the wire. The electric field points in one
direction down the length of the wire. The free electrons in the wire
feel a force from this electric field and speed up in the direction of
the field (in the opposite direction, actually, because electrons are
negatively charged). The electrons continue to collide with atoms, which
still causes them to bounce all around in different directions. But on
top of this random thermal motion, they now have a net ordered movement
in the direction opposite of the electric field. The electric current in
the wire consists of the ordered portion of the electrons' motion,
whereas the random portion of the motion still just constitutes the heat
in the wire. An applied electric field (such as from connecting a
battery) therefore causes an electric current to flow down the wire. The
average speed at which the electrons move down a wire is what we call
the "drift velocity".
Even though the electrons are, on average, drifting down the wire at the drift velocity, this does not mean that the effects
of the electrons' motion travels at this velocity. Electrons are not
really solid balls. They do not interact with each other by literally
knocking into each other's surfaces. Rather, electrons interact through
the electromagnetic field. The closer two electrons get to each other,
the stronger they repel each other through their electromagnetic fields.
The interesting thing is that when an electron moves, its field moves
with it, so that the electron can push another electron farther down the
wire through its field long before physically reaching the same
location in space as this electron. As a result, the electromagnetic
effects can travel down a metal wire much faster than any individual
electron can. These "effects" are fluctuations in the electromagnetic
field as it couples to the electrons and propagates down the wire. Since
energy and information are carried by fluctuations in the
electromagnetic field, energy and information also travel much faster
down an electrical wire than any individual electron.
The speed at which electromagnetic effects travel down a wire is
called the "signal velocity", "the wave velocity", or "the group
velocity". Note that some books insinuate that the signal velocity
describes a purely electromagnetic wave effect. This insinuation can be
misleading. If the signal traveling down an electric cable was an
isolated electromagnetic wave, then the signal would travel at the speed
of light in vacuum c. But it does not. Rather, the signal
traveling down an electric cable involves an interaction of both the
electromagnetic field fluctuations (the wave) and the electrons. For
this reason, the signal velocity is much faster than the electron drift
velocity but is slower than the speed of light in vacuum. Generally, the
signal velocity is somewhat close to the speed of light in vacuum. Note
that the "signal velocity" discussed here describes the physical speed
of electromagnetic effects traveling down a wire. In contrast, engineers
often use the phrase "signal speed" in a non-scientific way when they
really mean "bit rate". While the bit rate of a digital signal traveling
through a network does depend on the physical signal velocity in the
wires, it also depends on how well the computers in the network can
route the signals through the network.
Consider this analogy. A long line of people is waiting to enter a
restaurant. Each person fidgets nervously about in their spot in line.
The person at the end of the line grows impatient and shoves the person
in front of him. In turn, when each person in the line receives a shove
from the person behind him, he shoves the person in front of him. The
shove will therefore be passed along from person to person, forwards
through the line. The shove will reach the restaurant doors long before
the last person in line personally makes it to the doors. In this
analogy, the people represent the electrons, their arms represent the
electromagnetic field, and the shove represents a fluctuation or wave in
the electromagnetic field. The speed at which each person fidgets
represents the individual electron velocity, the speed at which each person individually progresses through the line represents the electron drift velocity, and the speed at which the shove travels through the line represents the signal velocity.
Based on this simple analogy, we would expect the signal velocity to be
very fast, the individual velocity to be somewhat fast, and the drift
velocity to be slow. (Note that in physics there is also another
relevant speed in this context called the "phase velocity". The phase
velocity is more of a mathematical tool than a physical reality, so I do
not think it is worth discussing here).
The individual electron velocity in a metal wire is typically
millions of kilometers per hour. In contrast, the drift velocity is
typically only a few meters per hour while the signal velocity is a
hundred million to a trillion kilometers per hour. In general, the
signal velocity is somewhat close to the speed of light in vacuum, the
individual electron speed is about 100 times slower than the signal
velocity, and the electron drift speed is as slow as a snail.
