How electricity REALLY travels at light speed

[stephen163]

When some people try to explain current flow in a circuit, their explanation troubles me. They say that electrons 'push against each other' and this is responsible for the close to speed of light propagation even when the electrons themselves are moving very slow.

My view is that though electrons may collide, the real reason that the effects of an electric circuit are almost instantaenous is because all electrons in the circuit are suddenly within an electric field - exterting a force, and the electric field itself travels at the speed of light. Nothing at all to do with electrons pushing, like water flowing out of a pipe.

Anyone agree/disagree?

 

[DaveC426913]

1] What does it mean in your model to "be in an electric field"?

2] In the classic model, how do the electrons push against each other?

 

[TurtleMeister]

Newton's cradle is usually used to demonstrate conservation of momentum and energy. However, I believe it can also be used as an analogy to demonstrate the speed of electricity through a conductor. Notice that the three center balls do not appear to move at all. And when one ball strikes, the other ball pops out almost instantly. In fact, if the balls are of exact equal mass and size, and are touching, then the kinetic energy will propagate through the center three balls at the speed of sound, while the outer two balls move much, much slower. I think that a very similar thing happens with an electric current, except that the energy is transferred at the speed of light instead of the speed of sound.

Edit:
After some investigation I now believe that the Newton's cradle analogy is incorrect. The motion and speed of (the electric signal) through a conductor appears to be governed by the electric field around the conductor.

 

[berkeman]

Careful Turtle, remember that electrons carry a charge. Their uncharged reaction cross-section is tiny compared to their charge interaction...

Dave's questions are on-point...

 

[DaveC426913]

2] In the classic model, how do the electrons push against each other?

My point is that electrons push against each other using their electric field; it's not as if they physically touch. So the question is: is your explanation actually explaining it any better, or is it a case of "same room, different lighting"?

 

[Bob S]

Hi stephen-
If by current flow you mean signal, the signal can travel at the speed of light. If you work out the Maxwell equations for a TEM (transverse electric magnetic) electronmagnetic wave in a coaxial transmission line with air dielectric, the speed of the signal is 1/sqrt(e₀u₀) which is by definition is the speed of light. In more common cables like RG-58, the signal is only about 2/3 c (8" per nanosecond).
Bob S

 

[stephen163]

The point I don't accept - and this is a point that is paraded as fact on many websites and textbooks, is that speed of light propagation of electricity is somehow just the same as Newton's cradle.

If you think about it, an electron at any point in a wire will experience the same electric field. At one end, it is being pushed quite strongly by the closer battery terminal, and pulled quite weakly by the one further away. In the middle of the wire, the push and the pull are equal. Anywhere in the wire, these 2 forces add up to the same value as they do in any other place in the wire. A constant electric field and electrons moving at all points in the wire, only limited in speed by the time it takes for the electric field from a negatively charge to influence a positive charge over a distance.

So speed of light propagation is not caused by a marble in a tube effect, or cars down a road, or water down a pipe, or Newton's cradle - rather it is the fact that every little charged particle has it's own little electric field and the speed at which this effects other little charged particles is the speed of light.

 

[f95toli]

The point I don't accept - and this is a point that is paraded as fact on many websites and textbooks, is that speed of light propagation of electricity is somehow just the same as Newton's cradle.

Of course it not the same. Newton's cradle is good analogy which can be used to explain why the field can propagate at c even though trhe electrons themselves do not. Not a real model.

But in order to explain what is really going you need need very advanced quantum mechanics. I say "very advanced" because even the quantum mechanical models you can find in graduate level solid-state physics books are really quite simplified in that they usually do not e.g. take different types of scattering into account. Unless you happen to specialise in the theoretical solid state physics it is very unlikely that you will ever be exposed to models that even try to be accurate enough to allow you to calculate electrical properties of metals from first principles (which requires numerical methods).

I did my PhD working on superconductors and have a pretty good idea about BCS theory etc. But superconductors are much easier to understand that real metals (which is why BCS theory works so well); I guess you could say I know enough about the physics of electrons in metals to know that I don't much about it.

 

[DaveC426913]

...every little charged particle has it's own little electric field and the speed at which this effects other little charged particles is the speed of light.

This description here boils down to "the electrons push against each other with their electric repulsion, not with any physical contact."

I don't think anyone has trouble with this concept.

 

[stephen163]

I believe Newton's cradle is a misleading analogy. The situation may be complicated at a quantum level, but on a macroscopic level, I don't see how it's any more complicated than a sea of electrons drifting together under the influence of an applied electric field. The electric field travels at light speed so the effect from the battery will be felt by all electrons in the wire almost instantaneously.

It's not the first electron moves a bit, pushes another, which pushes another all the way down the conductor. In the time it takes the first electron to collide with any other, the electric field has already influenced every single free electron in the entire conductor.

 

[f95toli]

I believe Newton's cradle is a misleading analogy. The situation may be complicated at a quantum level, but on a macroscopic level, I don't see how it's any more complicated than a sea of electrons drifting together under the influence of an applied electric field.

There is no "macroscopic level" here. Electrical conduction is ALWAYS a quantum mechanical phenomenon. The simplest model for a "real" metal is the Bloch model, in which you basically solve the Schrödinger equation for a periodic potential. This is still a gross simplification but it is still much closer to what is "really" going on than any model that treats electrons as individual "balls". The essential point here is that the "wave nature" (a term I don't really like) of the electrons is extremely important.
One example of this is that electrons in a perfect lattice would -at least if you neglect e-e effects - travel without ANY resistance; i.e. there is no scattering in a perfect period potential because the solutions are Bloch waves. This would certainly not be true if electrons were just "balls" moving through a lattice, since they would then be scattered by the potential of the ions.

There is a whole chapter on the "Failure of the free electron model" in Ashcroft-Mermin (a standard text on condensed matter physics)

Edit: Grammar and typos

 

[Bob S]

It is useful to consider how the current flows in a circuit, or in a coaxial transmission line, when the conductors are all superconductors, so there are no electric fields inside, and no current penetration into the superconductor (type I, no Meissner effect). So there is no electric field in the conductor to "push" the electrons. Review of Maxwell's equations and the derivation of the Poynting vector concept shows that the signal power, and hence the signal itself, actually flows between the conductors (the E and H fields), and therefore the signal's characteristics are determined by the wire inductance L (e.g., the wire diameter) per unit length, and the shunt capacitance C (e.g. dielectric constant of the material) per unit length between the conductors.
Bob S