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What is the speed of electricity?
Category: Physics
Published: February 19, 2014
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and physics professor at West Texas A&M University
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 billion 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.