How Fast Does an Electrical Impulse Travel in a Copper Wire?

[Dale]

Yes he does, he's clearly refers to electrons

Yes, but he also clearly says that they are pushed out of one terminal and allowed into the other terminal. That is not electrons moving both directions. So when this process meets in the middle it is not electrons moving both directions meeting in the middle.

 

[Dale]

And in fact, I am asking if there is any difference at all?

The difference is using only Gauss’ law or using all four of Maxwell’s equations. The partial derivative wrt time is non zero for both E and B, so you have to use all four.

 

[vanhees71]

Of course, you have to use all 4 Maxwell equations. The result is the "telegrapher's equation" (Heaviside) or a more elaborate wave equation in presence of the conductors (H. Hertz, who had a hard time trying to formulate it for infinitely thin wires; see Sommerfeld vol. 3 for details), and as was stated correctly several times in the very beginning of the thread, the signal velocity is the propagation velocity of the em. field and not the drift velocity of the electrons which is tiny (about 1mm/s). Also the energy transport is through the fields and not through the drift of the electrons in the wire.

 

[nsaspook]

I am not quite convinced. If we assume that the free (or nearly free) electron model holds, then the electrons are fermions which are indistinguishable and delocalized. The ones responsible for electric conduction move at speeds comparable to about 1/100 th of c (i.e. at Fermi velocity).

In a conventional vacuum tube the free electrons from the cathode are accelerated to the anode often at a sizable fraction of C. What happens to the kinetic energy of those electrons when they hit the anode? The main problem with using a physical electron transfer for electrical energy is you don't actually get current electricity energy as the end product.

 

[jartsa]

I am not sure it directly enters into computations.
You could transmit electricity via a metallic conductor, like a copper wire wrapped in rubber insulator, where electrons are charge carriers and move. Or you could transmit electricity through nonmetallic conductor, like the same rubber hose containing not metal copper wire, but aqueous solution of copper sulphate. In which electrons cannot move, and charge carriers are copper cations of far bigger mass. When you measure travel time of switching surges and lightning surges, does the mass of charge carrier enter directly into equations?

https://en.wikipedia.org/wiki/Telegrapher's_equations#Role_of_different_components

Wikipedia says there that inductance makes it look like current has inertia, and that large inductance makes the wave move more slowly, just as waves travel more slowly down a heavy rope than a light one.I would just say that when charges have inertia, then wave moves slowly.

Anyone have some idea about when does the mass-inertia become significant compared to the inductance-inertia?

 

[Byron Forbes]

Of course, you have to use all 4 Maxwell equations. The result is the "telegrapher's equation" (Heaviside) or a more elaborate wave equation in presence of the conductors (H. Hertz, who had a hard time trying to formulate it for infinitely thin wires; see Sommerfeld vol. 3 for details), and as was stated correctly several times in the very beginning of the thread, the signal velocity is the propagation velocity of the em. field and not the drift velocity of the electrons which is tiny (about 1mm/s). Also the energy transport is through the fields and not through the drift of the electrons in the wire.

There has been some confusion about drift velocity in this thread, but not from me.

My suggestion is simple -----> the speed of electricity in a wire is a product of a longitudinal wave traveling through the electrons.

 

[f95toli]

I would just say that when charges have inertia, then wave moves slowly.

Anyone have some idea about when does the mass-inertia become significant compared to the inductance-inertia?

It depends. There are a few materials where the "kinetic inductance" can be very significant. "kinetic" here means that the inductance can indeed come the inertia of particles with a large effective mass; an example would be ballistic transport in some clean semiconductors.
However, kinetic inductance is most prominent in certain superconductors (e.g. NbN and TiN) when they are made into very thin films (~10 nm). Here the process is much more difficult to visualise (as should be evident from the fact that the kinetic inductance is strong function of film thickness). These materials are very useful because it allows us to make very small microwave filters, resonators etc since we don't need to rely on geometric inductors (such as spirals or meander) which are inevitable quite big.

 

[Byron Forbes]

It depends. There are a few materials where the "kinetic inductance" can be very significant. "kinetic" here means that the inductance can indeed come the inertia of particles with a large effective mass; an example would be ballistic transport in some clean semiconductors.
However, kinetic inductance is most prominent in certain superconductors (e.g. NbN and TiN) when they are made into very thin films (~10 nm). Here the process is much more difficult to visualise (as should be evident from the fact that the kinetic inductance is strong function of film thickness). These materials are very useful because it allows us to make very small microwave filters, resonators etc since we don't need to rely on geometric inductors (such as spirals or meander) which are inevitable quite big.

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

 

[Dale]

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

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.

 

[nsaspook]

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

I don't because I don't really know what you mean by 'electricity'. In science current 'electricity' is normally expressed as a rate in the coulomb.

The coulomb is defined as the quantity of electricity transported in one second by a current of one ampere.

 

[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?

 

[Byron Forbes]

I don't because I don't really know what you mean by 'electricity'. In science current 'electricity' is normally expressed as a rate in the coulomb.

https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of-electricity/

1. The individual electron velocity
2. The electron drift velocity
3. The signal velocity

This thread is about 3.

 

[Dale]

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.

 

[Byron Forbes]

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! :)

 

[Dale]

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.

 

[Byron Forbes]

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! :)

 

[Dale]

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

Please post your professional scientific source for this supposed "proof".

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

 

[Byron Forbes]

Please post your professional scientific source for this supposed "proof".

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?

 

[Dale]

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

 

[nsaspook]

https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of-electricity/

1. The individual electron velocity
2. The electron drift velocity
3. The signal velocity

This thread is about 3.

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.

 

[Byron Forbes]

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?

 

[Dale]

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.

 

[Byron Forbes]

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?

 

[Dale]

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)?

 

[Byron Forbes]

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?

 

[Dale]

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.

 

[nsaspook]

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

 

[snorkack]

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.

 

[Dale]

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.

 

[anorlunda]

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."