# Speed of "Electricity"

• Byron Forbes
Yes. Did you see the point I made above?

As I said already multiple times, your idea just doesn’t work. Since this is dynamic you have to use all four Maxwell’s equations, not just Gauss law.

Ok, so what do you mean?

That I need to add in a little induction?

Ok, so what do you mean?

That I need to add in a little induction?
I mean that you are thinking of a purely "electrons pushing each other" explanation. That is governed by Gauss' law. But Gauss' law is insufficient to explain EM behavior for changing fields. When you have non-zero time derivatives then you need Faraday's law and Ampere's law also. That gives you EM waves.

Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.

• nasu and Delta2
Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.

Hmmmm, let me see now. I know the mass of the electron.

Speed of sound (c) in a medium - where
• Ks is a coefficient of stiffness, the isentropic bulk modulus (or the modulus of bulk elasticity for gases);
• ρ is the density.

So now I simply need a way to think of conduction electrons as a medium, giving me p, and then the E field as the Ks and I'm good to go! :)

Maybe I can take a page out of QM, reverse engineer everything, playing around with the parameters and variables until everything comes out exactly the way I want it to, and then go and collect my Nobel prize! :)

• davenn
Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.
The speed of a longitudinal wave is given by ##\sqrt{K/\rho}## where ##K## is the bulk modulus and ##\rho## is the density. For the electrons in a copper conductor ##K=1.4 \ 10^{11}\text{ N/m}^2##, and ##\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}## so ##\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c##. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

• • nasu, Delta2, etotheipi and 1 other person
I mean that you are thinking of a purely "electrons pushing each other" explanation. That is governed by Gauss' law. But Gauss' law is insufficient to explain EM behavior for changing fields. When you have non-zero time derivatives then you need Faraday's law and Ampere's law also. That gives you EM waves.

As already mentioned, and proven, it is electron movement first and EM later. The EM part plays no role in the point I'm making whatsoever apart from a little inductance, which also does nothing to undermine the point.

Again, when you first turn on a power supply, the onset of electron movement at any part of the wire is dictated by a wavefront (not EM) that is simply longitudinal! i.e. a longitudinal wave traveling through the electrons, exactly the same as a sound wave.

It just is! :)

• davenn
As already mentioned, and proven, it is electron movement first and EM later.

In addition to violating Maxwell's equations, your idea does not appear to explain the following:
1) the speed of the EM waves
2) the dependence on the conductor geometry
3) the dependence on the dielectric outside the conductor

• vanhees71

My capacitor example.

But if you want to tell us about this mysterious EM wave that is apparently in existence before any electron even moves, then I'm all ears.

Just to be clear - are you suggesting that signal velocity is in no way related to the forces of repulsion between electrons?

Just to be clear - are you suggesting that signal velocity is in no way related to the forces of repulsion between electrons?
No, I am not suggesting that at all. Gauss' law is part of Maxwell's equations. It is just not all of Maxwell's equations. You need all of Maxwell's equations.

Your personal capacitor example is insufficient. You need an actual scientific reference

Your personal capacitor example is insufficient. You need an actual scientific reference

How about something like a paper on the Michelson-Morely Experiment that leads to the debunking of The Luminiferous Aether? Is that the type of thing you mean?

How about something like a paper on the Michelson-Morely Experiment that leads to the debunking of The Luminiferous Aether? Is that the type of thing you mean?
No. I mean a paper that claims, as you do, that the velocity of the signal in the wire is due entirely to longitudinal current waves as you have described. Such waves would be based on Gauss' law (or equivalently Coulomb's law) and Ohm's law and the Lorentz force only.

Then this thread is not about the speed of 'electricity' as a thing, it's about electrical science, the speed of EM waves and mass-less particles.

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?
The question is not whether or not they are moving. It is a question of why they are moving. Is it due to Gauss' law (longitudinal current wave) or all of Maxwell's equations (EM wave)?

The question is not whether or not they are moving. It is a question of why they are moving. Is it due to Gauss' law (longitudinal current wave) or all of Maxwell's equations (EM wave)?

So you are suggesting that it is possible that signal speed is entirely unrelated to the forces of repulsion between electrons?

So you are suggesting that it is possible that signal speed is entirely unrelated to the forces of repulsion between electrons?
I already told you that I am not suggesting that (see post 79). You are apparently missing some of my posts above. In particular, did you miss the calculation of the speed of the longitudinal waves above (see post 75)? That is pretty conclusive that your approach does not work.

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?

By analogy what is the velocity of water (electrons) when a rock (signal energy) skips above it? Just like in electric circuits, signals are all about energy and the speed of that energy, not charge (electricity) in a system of wires that guides (and modifies the speed of energy vs pure vacuum) electrical energy in space. We normally design signal circuits to reduce the amount of energy in charge (electrons) to the lowest point possible unless we need to generate heat or utilize the particle KE in things like semiconductor doping.

The fact that the signal velocity of the EM field is much higher than the electron drift speed means we can have charge separation across the length of a wire (a good conductor with lots of free electrons) in things like a simple antenna of a single wire. The electrons can't move at the speed needed to keep the conductor neutral in response to the changing fields surrounding it so we have a phase shift of the applied potential across the single wire. This is a needed condition for EM radiation where the wire charges just giggle back and forth very small distances while energy flows continuously forward from the RF energy source to free space.

Even in a AC circuit (50/60Hz) without EM radiation we have the same effect of wire charges just giggle small distances while the signal energy flows in one direction continuously from source to load.
http://amasci.com/elect/poynt/poynt.html
http://amasci.com/miscon/speed.html

Last edited:
Consider a telegraph circuit. A battery. Two insulated wires. A telegraph key on another continent. And a measuring device.
In silent condition, there is no current, and no magnetic field. There IS electrostatic field between two wires, and each wire to infinity - for the potential of each wire is different from other wire as well as infinity.
When the key is pressed, what changes?
Electrostatic field between wires existed before pressing the key. There was electrostatic field between the open sides of switch, it just caused no current. When switch is closed, the change is in electron movement. Therefore electron movement must be the cause of electromagnetic field, not vice versa.

When switch is closed, the change is in electron movement. Therefore electron movement must be the cause of electromagnetic field, not vice versa.
The other change that you neglected to mention is in the magnetic field. (Edit: actually, the E field changes too, both inside and outside the wire)

The question is what causes the signal to propagate to the next part of the cable after the first bit of current. Is it purely due to Gauss’ law (the electrical equivalent of an acoustic wave) or is it necessary to include the rest of Maxwell’s equations?

I think it is pretty clearly the latter.

• Forgive me from being almost off-topic, but this thread reminds me of the following true anecdote.
From: Edison, His Life and Inventions by Dyer, Frank Lewis; Martin, Thomas Commerford.

Edison was now asked if he thought he could get a greater speed through submarine [telegraph] cables with this system than with the regular methods, and replied that he would like a chance to try it. For this purpose, twenty-two hundred miles of Brazilian cable then stored under water in tanks at the Greenwich works of the Telegraph Construction & Maintenance Company, near London, was placed at his disposal from 8 P.M. until 6 A.M. "This just suited me, as I preferred night-work. I got my apparatus down and set up, and then to get a preliminary idea of what the distortion of the signal would be, I sent a single dot, which should have been recorded upon my automatic paper by a mark about one-thirty-second of an inch long. Instead of that it was twenty-seven feet long! If I ever had any conceit, it vanished from my boots up. I worked on this cable more than two weeks, and the best I could do was two words per minute, which was only one-seventh of what the guaranteed speed of the cable should be when laid. What I did not know at the time was that a coiled cable, owing to induction, was infinitely worse than when laid out straight, and that my speed was as good as, if not better than, with the regular system; but no one told me this."

• hmmm27, Dale and Delta2
Forgive me from being almost off-topic, but this thread reminds me of the following true anecdote.
Good example. That result cannot be explained only by current pushing inside the wire.

Therefore electron movement must be the cause of electromagnetic field, not vice versa.
I think that's half the truth only. The other half is that the field affects or causes the current. It's a dynamic relation between the current and the field that works in both ways: current->field but also field->current so it is actually current<->field.

• Dale
Forgive me from being almost completely off-topic, but this thread reminds me of a story I heard. Google:

only there is no cat einstein

The attribution to Einstein is certainly false, maybe it should have been Maxwell .

I already told you that I am not suggesting that (see post 79). You are apparently missing some of my posts above. In particular, did you miss the calculation of the speed of the longitudinal waves above (see post 75)? That is pretty conclusive that your approach does not work.

Yes, I did miss that somehow. Is there delays in posts appearing on here at times? Anyway, I'll respond to that now.

• Dale
In the following link, there is an explanation of plasmon oscillations, where an electron in a metal can mechanically vibrate at optical frequencies. This does not agree with the constraints imposed by the mechanical model mentioned in Post 75. If an electron can vibrate at such frequencies, it seems likely that it can form a transmission medium.

• Byron Forbes
I think that's half the truth only. The other half is that the field affects or causes the current. It's a dynamic relation between the current and the field that works in both ways: current->field but also field->current so it is actually current<->field.

I disagree with this completely.

Clearly, everything is initiated by electron movement. At that time you get a little inductance, depending on the magnitude of the acceleration of an electron. This would slow down the propagation because it is akin to increasing the mass of an electron. i.e. it is akin to increasing the density of a medium sound might travel through, thus yielding a slower speed.

Any other effect you might want to introduce, and I don't know what it would be, is surely not going to happen before or instead of the forces of repulsion between the electrons.

Lets take a length of wire and touch it against an object with static electricity. At the moment of touching, an electron flows from the object into the wire. At the onset, there is no EM wave. All there is is that electron accelerating toward another and an increase in the force of repulsion between them. How could any other force be in play? Clearly, if any EM effects are the result of the electron acceleration, they are neither happening before or even during the onset of acceleration. At a time shortly after the onset of acceleration there would be inductance from lateral electrons. But this inductance simply means a lesser resultant E field of repulsion.

The electrons push the ones ahead of them through the wire - the EM is a product of this and plays zero roll in it other than inductance.

• • weirdoguy and davenn
The speed of a longitudinal wave is given by ##\sqrt{K/\rho}## where ##K## is the bulk modulus and ##\rho## is the density. For the electrons in a copper conductor ##K=1.4 \ 10^{11}\text{ N/m}^2##, and ##\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}## so ##\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c##. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

@Byron Forbes didn't mention this important thing:

Bulk modulus of copper is a measure of how much energy is needed to force some more copper atoms into some volume filled with copper.

Energy needed to force some more electrons into some volume filled with copper is much larger. This latter "bulk modulus" is relevant here.

(Let's assume that the lattice of positive charges just stays still when an electron density wave is passing through a wire)

Last edited:
• Byron Forbes
The speed of a longitudinal wave is given by ##\sqrt{K/\rho}## where ##K## is the bulk modulus and ##\rho## is the density. For the electrons in a copper conductor ##K=1.4 \ 10^{11}\text{ N/m}^2##, and ##\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}## so ##\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c##. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

There are values for the electron density in a conductor that make it the same as the density of a medium that might carry air? And also values for it's bulk modulus in the same manner?

I doubt this very much but I'd be happy for you to point these out to me so that I can see who worked this out and how.

Do you have a scientific paper? :)

• • weirdoguy and davenn
Energy needed to force some more electrons into some volume filled with copper is much larger. This latter "bulk modulus" is relevant here.
They are essentially the same. It is not much larger. This should not be too surprising since most of the properties of a material are related to its electrons and how they interact with each other and with the nuclei.

Last edited:
Good example. That result cannot be explained only by current pushing inside the wire.

Assuming I'm interpreting that story properly, you can.

There is a ton more inductance, akin to making the electrons heavier, and so the longitudinal wave travels slower. Or the modulus less - either way, electron acceleration is less and so a slower longitudinal wave.

It is always a case of electron repulsion minus inductance, which simply adds up to a reduced force of repulsion.

• • weirdoguy and davenn
There are values for the electron density in a conductor that make it the same as the density of a medium that might carry air?
Yes, that should be obvious. Electrons have very little mass relative to the nucleus and conduction electrons have about the same number density as the nuclei.

I doubt this very much but I'd be happy for you to point these out to me so that I can see who worked this out and how.

Do you have a scientific paper? :)
Sure, this is part of a standard classroom exercise, lecture notes, and standard published data:

##K=1.4 \ 10^{11}\text{ N/m}^2## from exercise 4 at http://www-sp.phy.cam.ac.uk/~je102/CMP/CMP_Examples_2_2008-9.pdf

##8.94 \ 10^{28}\text{ e/m}^3## from slide 15 http://web.mst.edu/~vojtat/class_2135/lectures/lecture10/lecture10.pdf

## \ 9.1 \ 10^{-31} \text{ kg/e}## https://physics.nist.gov/cgi-bin/cuu/Value?me

Anyway, since even after 100 posts you still have yet to provide any scientific support for your position we will consider the matter closed. If you would like to reopen it please do so with said support. You have been adequately instructed here and there is really nothing more to discuss.

• • davenn, berkeman, weirdoguy and 3 others