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

[Dale]

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.

 

[Delta2]

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.

 

[gmax137]

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 .

 

[Byron Forbes]

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.

 

[tech99]

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.

 

[jartsa]

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)

 

[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? :)

 

[Dale]

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.

 

[Byron Forbes]

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.

 

[Dale]

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.