electromagnetism - How fast does electricity flow?

I get confused on the low-level physics of electricity from time to time. It came up in "Which way does electricity power a circuit," and I don't totally get it.

How fast does electricity flow? Is the speed of an electron different in say a resistor than in a wire? Does it matter? Or are the effects of the electron the only important thing, with lower levels of abstraction not useful in practice?

I know there are already materials on this topic, and I have read some of them. I think having the question on this site might inspire some interesting answers to the age-old question.

Bonus points for:

• Identifying and clearing up common misconceptions


• Explaining in a way that someone with a high school diploma could understand, without oversimplifying it so much that its incorrect

Answer

How fast does electricity flow? This is a good question, because it seems like a simple enough question, but usually it indicates some underlying misconceptions. The first difficulty in answering the question is knowing, what is electricity? Do you mean:

1. How fast do changes in electrical fields propagate? or...


2. How fast do electrical charge carriers move?

Usually, people asking this question actually care about the former, but are thinking about the latter. However, not having a clear understanding of the difference, their underlying concern actually can't be addressed without stepping back and addressing the underlying misconceptions which lead to the question.

Understand is this: there are forces, and there are things that transmit forces, and they are not the same thing. Here's an example: I'm holding one end of a rope, and you are holding the other end. When I want to get your attention, I tug the rope. There is the rope, and there is the tug. The tug travels as a wave of force down the rope at the speed of sound in the rope. The rope itself will move at some other speed.

Say I have two lookout towers, and when I see the approaching invaders, I shout to the other tower. Sound will travel as waves in the air at the speed of sound. How fast are the molecules in air moving? Do you care?

Some people won't let this go until the motion of the molecules is actually explained, even though it's usually not relevant to their concerns. So here's the answer: the molecules are flying around in all random directions, all the time. They fly around because they have non-zero temperature. Some are very fast. Some are very slow. They bump into each other all the time. It's very random.

When you shout, your vocal tract compresses (and rarefies, as your vocal cords vibrate) some of the air. The molecules in this compressed region want to move to a region with less pressure, so they do. But now this nearby region has too much air, and is a little more compressed than the air around it, so the compressed region expands outward a little more. This wave of compression moves through the air at the speed of sound.

All of this happens superimposed on the random motion of the molecules previously mentioned. It's unlikely that the same molecules that were in your vocal tract will be the ones that vibrate in the listener's ear. If you watch individual molecules, you will observe them going in all directions. Only if you observe a lot of them will you notice that slightly more went in one direction versus another. It is true for all things we would call "sound" that the random motion of the molecules due to thermal noise is much more than their motion due to sound. When the "sound" becomes the more relevant motion, we tend to call it not "sound" but rather an "explosion".

The situation with electricity is not much different. A metal conductor is full of electrons that are free to wander around the entire circuit in random directions, and they do, simply because they are warm. Things in our circuits make waves in this sea of electrons, and these waves propagate at the speed of light¹. At the currents we typically encounter in circuits, most of the electron motion is due to thermal noise.

So now we can answer the questions:

How fast do changes in electrical fields propagate? At the speed of light in the medium in which they are propagating. For most cables, this is in the neighborhood of 60% to 90% of the speed of light in a vacuum.

How fast do electrical charge carriers move? The velocities of individual charge carriers are random. If you take the average of all these velocities, you can get some velocity that depends on the charge carrier density, and the current, and the conductor's cross-sectional area, and it's typically less than a few millimetres per second in a copper wire. Above that, resistive losses become high in ordinary metals and people tend to make the wires bigger instead of forcing the charges to move faster.

Further reading: Speed of Electricity Flow by Bill Beaty

^{1: The speed of light depends on the material in which the light is propagating, just as with sound. See Wave propagation speed.}