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

[Byron Forbes]

2 questions to all atm.

1. Is the implication here that current is produced due to an EM wave and that the notion of 2 electrons becoming closer to each other, thus pushing each other harder (force of repulsion of the respective electric fields) plays absolutely no role in the production of current?

2. If electrons weighed more, would the speed of electricity in a wire be less?

A few other notes -

The idea that an E field is set up immediately all around the wire is wrong. If that was the case then there would be no such thing as signal speed.

The implication that there is an EM wave dictating everything seems weird. It's as if it is being suggested that this wave comes first and then the current results from that rather than the other way around! What if the entire current began with a capacitor for example - clearly that would be a case of electron movement first and then everything following on from that, wouldn't it?

 

[snorkack]

If we make the amount of charges in the 'wire' small enough, then a normal power source can make the charges move like the magnets in the video, or faster. The mass of electron would be important in that case.

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?

 

[anorlunda]

When you measure travel time of switching surges and lightning surges, does the mass of charge carrier enter directly into equations?

The constants $\mu_0$ and $\epsilon_0$ in Maxwell's Equations that govern the propagation.

For a mechanical motion model of conduction that does include mass (but not propagation of the field), see https://en.wikipedia.org/wiki/Drude_model

 

[snorkack]

The constants $\mu_0$ and $\epsilon_0$ in Maxwell's Equations that govern the propagation.

Maxwell equations are inapplicable. No 0 here, because no vacuum, nothing constant about μ or ε in terms of location or direction.

 

[anorlunda]

The values of μ or ε are different in different media. Maxwell's Equations apply everywhere.

 

[nsaspook]

The implication that there is an EM wave dictating everything seems weird. It's as if it is being suggested that this wave comes first and then the current results from that rather than the other way around! What if the entire current began with a capacitor for example - clearly that would be a case of electron movement first and then everything following on from that, wouldn't it?

First it should be clear that electricity (physics meaning) refers to the movement of charge carriers not the electrical (electromagnetic) energy as they are measured in two separate terms.

The implication is see in some is that the EM wave and good conductor electron movements are somehow separate events in this wiring circuit. They are a system/synergy, a wave-guide for electrical energy that usually also imparts (electrical energy is transformed) a small amount of kinetic energy to the charge carriers that's usually wasted as heat called resistance. This guided by conductors near-field EM field/wave can be mostly reactive, closely coupled to the conductors, sources and currents instead of a typical far-field EM wave that mainly exists uncoupled from the sources and currents as it propagates.

 

[snorkack]

A conductor does not seem to even have ε. Because, in long term, there will be no electric field in the conductor. In short term, there is, because inductivity and resistivity will resist the currents that tend to destroy the electric field.

 

[Byron Forbes]

Here's an attempt to bring this discussion back into focus.

Consider a power supply (PS) connected to a loop of wire - basically, out of one terminal, electrons are pushed out, and in the other they are allowed in. This current is not immediately observed all around the wire. The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

As is obvious, this process will proceed around the wire in either direction and meet half way along the wire. In a typical DC circuit, shortly after this event, assuming we continued to apply a steady electric field at our PS, we'd end up with a steady DC current.

Now let's consider a point on the wire 1/4 of the way around where the electrons are headed toward us from the PS. At a point in time, dictated by the speed of electricity in this particular wire, we would see an electron that has just begun to move alongside an electron that has yet to move. So the main question this thread is asking, is why and how does the stationary electron begin to move.

My assertion is that it's exactly the same as a longitudinal wave, like a sound wave in water or air, traveling through the electrons. So the moving electron becomes closer to the stationary one, the force of repulsion between them increases as a result, and so now the stationary electron accelerates away from it. Then we move to the next electron in line, and so on and so forth, all around the wire.

But this apparently is not the right thinking. In fact, it seems to be suggested that the forces of repulsion between the electrons plays absolutely no roll in this process at all. This makes no sense to me at all!

 

[davenn]

Consider a power supply (PS) connected to a loop of wire - basically, out of one terminal, electrons are pushed out, and in the other they are allowed in. This current is not immediately observed all around the wire. The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

Serious mis-conseptions in there

As is obvious, this process will proceed around the wire in either direction and meet half way along the wire. In a typical DC circuit, shortly after this event, assuming we continued to apply a steady electric field at our PS, we'd end up with a steady DC current.

Absolutely NOT, completely incorrect

Now let's consider a point on the wire 1/4 of the way around where the electrons are headed toward us from the PS. At a point in time, dictated by the speed of electricity in this particular wire, we would see an electron that has just begun to move alongside an electron that has yet to move. So the main question this thread is asking, is why and how does the stationary electron begin to move.

OK, what you haven't seemed to have picked up yet is that it's the electric field propagating around the circuit, on the OUTSIDE of the wire,
at a bit less than c, that "drives" the electrons/charge carrier movement through the wire.
As some one mentioned, way back, early on page one of this thread, If the electric field didn't propagate at something close to the speed of light, then the light globe 1/2 way ( or where-ever) around the circuit wouldn't switch on so quickly after power was applied to the circuit.

Electrons/charge carriers WILL start moving under the influence of the electric field as soon as the field reaches them.
Again, as has been said several times, electron velocity IN the wire is VERY slow, ~ 1 to 2 mm/sec, compared to the substantially higher
velocity of the electric field around the outside of the wire.
So The light globe is initially lit, by the electrons that are present in the filament ( at rest/ t=0) and start moving when the electric field reaches them.

Whether the electrons are pushed, dragged (or something else) into motion by the electric field, I am not sure.
@Dale or one of our other senior dudes can probably answer that ?

Dave

 

[Delta2]

Here's an attempt to bring this discussion back into focus.

Consider a power supply (PS) connected to a loop of wire - basically, out of one terminal, electrons are pushed out, and in the other they are allowed in. This current is not immediately observed all around the wire. The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

As is obvious, this process will proceed around the wire in either direction and meet half way along the wire. In a typical DC circuit, shortly after this event, assuming we continued to apply a steady electric field at our PS, we'd end up with a steady DC current.

Now let's consider a point on the wire 1/4 of the way around where the electrons are headed toward us from the PS. At a point in time, dictated by the speed of electricity in this particular wire, we would see an electron that has just begun to move alongside an electron that has yet to move. So the main question this thread is asking, is why and how does the stationary electron begin to move.

My assertion is that it's exactly the same as a longitudinal wave, like a sound wave in water or air, traveling through the electrons. So the moving electron becomes closer to the stationary one, the force of repulsion between them increases as a result, and so now the stationary electron accelerates away from it. Then we move to the next electron in line, and so on and so forth, all around the wire.

But this apparently is not the right thinking. In fact, it seems to be suggested that the forces of repulsion between the electrons plays absolutely no roll in this process at all. This makes no sense to me at all!

I can't find exactly where the flaw is with this microscopic electromechanical model (each electron moves and its movement signals the nearby electrons).

However we know by transmission line theory wave equations that the voltage and current in a transmission line constitute waves that travel at a speed that is a significant fraction of speed of light (66%-99% of speed of light) and these equations are known from Olivier Heaviside back at 1885, he developed them starting from Maxwell's equations, without the knowledge of this underlying microscopic model of electrons about 15 years before the electron was discovered.

 

[jartsa]

So the main question this thread is asking, is why and how does the stationary electron begin to move.

Well I guess the electric fields of other electrons is the reason why the stationary electron starts to move.

If we study the electric field outside the wire, first we notice that it exists, and it has energy. Well, that's because the electrons 'inside' the wire exist outside the wire too, I mean their fields stick out of the wire.

What I'm saying is that the energy of the pressure wave traveling through a wire is mostly outside the wire.

You see, I'm trying to combine the two apparently disagreeing ideas here, the idea of an EM-wave outside the wire, and the idea of a pressure wave inside the wire.

 

[Dale]

As is obvious, this process will proceed around the wire in either direction and meet half way along the wire.

Absolutely NOT, completely incorrect

Well, I am kind of in between here. It is not guaranteed to happen that way, but there are circumstances where it could happen that way, so I don’t think that either “obvious” or “completely incorrect” is quite right. Since it could happen that way and since this is the OP’s thread I think we should go ahead and consider such a scenario, remembering that it is only one of several possible scenarios.

So the main question this thread is asking, is why and how does the stationary electron begin to move.

That is easy and clear. It moves when the E-field exerts a force on it.

I think that your actual question is where that E-field comes from? Is it due simply to Coulomb repulsion or is it due to waves outside the wire?

Coulomb repulsion is Gauss’ law, and Gauss’ law is an essential part of Maxwell’s equations. So the Coulomb repulsion is certainly part of the explanation.

However, Gauss’ law by itself is insufficient to explain a dynamic scenario with time varying E and B fields. That requires all four of Maxwell’s equations. So Gauss’ law is indeed an essential part of the explanation, it is just not the whole explanation by itself.

 

[davenn]

, but there are circumstances where it could happen that way,

ohhh ? being which ?
in all my years on here and other physics teaching, never heard of electrons traveling both
directions and meeting in the middle ?

They can change direction as with AC, but traveling in opposite directions at the same time and meeting in the middle ?

 

[Dale]

ohhh ? being which ?
in all my years on here and other physics teaching, never heard of electrons traveling both
directions and meeting in the middle ?

That isn’t what he said. He said electrons being pushed out of one terminal and allowed into the other terminal. So what he is describing is a scenario where current is going in one terminal and out the other while there is still no current in the far part of the loop.

That can happen eg when a large loop starts at 0 V for a long time and then the positive terminal is stepped up to 5 V and the negative terminal is stepped down to -5 V

 

[davenn]

That isn’t what he said. He said electrons being pushed out of one terminal and allowed into the other terminal.

ummmm not really, he said ...

As is obvious, this process will proceed around the wire in either direction and meet half way along the wire. In a typical DC circuit, shortly after this event, assuming we continued to apply a steady electric field at our PS, we'd end up with a steady DC current.

Nothing meets in the middle ( half way along), but regardless ... he had the idea not quite right as he doesn't realize how quickly the E field propagates around a circuit ...

The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

As the electrons/charge carriers start moving as soon as they are influenced by the electric field, which for anything other than longer transmission lines is just short of instantaneous and not delayed as much as what he thinks. That is, when he flicks the light switch on at home, the light comes on from a human observational ( non-instrument measured) point-of-view "instantaneously"

 

[Dale]

ummmm not really, he said ...

You have to look at the previous paragraph to see what he means by “this process”. His “this process” is not electrons moving both directions and meeting in the middle. He never says that.

Nothing meets in the middle ( half way along)

Waves propagating from both terminals certainly can meet in the middle, depending on the geometry and the setup.

 

[davenn]

You have to look at the previous paragraph to see what he means by “this process”. His “this process” is not electrons moving both directions and meeting in the middle. He never says that.

Yes he does, he's clearly refers to electrons

Consider a power supply (PS) connected to a loop of wire - basically, out of one terminal, electrons are pushed out, and in the other they are allowed in. This current is not immediately observed all around the wire. The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

 

[snorkack]

However we know by transmission line theory wave equations that the voltage and current in a transmission line constitute waves that travel at a speed that is a significant fraction of speed of light (66%-99% of speed of light) and these equations are known from Olivier Heaviside back at 1885, he developed them starting from Maxwell's equations, without the knowledge of this underlying microscopic model of electrons about 15 years before the electron was discovered.

Because they don´ t depend on whether the charge carriers in wire are electrons, holes or heavy ions?

But with instruments, speed of electricity is clearly not instant.

Water notoriously has ε as much as 81 (and 87 at 0 degrees).
When you try to send a telegram, or a ping, to the opposite side of Earth, like New Zealand to Spain, does your ping travel in direct line? That would be 43 ms. Through Earth core. Or does it travel around Earth? 67 ms at speed of light. Or does it follow the detours of cables under sea?
And at what speed? Since water has ε of 81, does the polarization of the sea around your ping traveling along cable (inside insulation) slow it down to 1/9 speed of light?

 

[tech99]

The idea that an E field is set up immediately all around the wire is wrong. If that was the case then there would be no such thing as signal speed.

The implication that there is an EM wave dictating everything seems weird. It's as if it is being suggested that this wave comes first and then the current results from that rather than the other way around! What if the entire current began with a capacitor for example - clearly that would be a case of electron movement first and then everything following on from that, wouldn't it?

Yes I agree with htis statement. To clarify my own thinking slightly, I imagine a wire spaced a long way from other conductors. I charge up an object such as a sphere and touch the end of the wire with it. Now we have a step impulse applied to the line, causing the first electrons to move and create magnetic fields surrounding the wire. As these first electrons move towards other electrons, we see repulsion and so on. As time goes on, the high frequency components of this discharge decay and we see progressively lower frequencies being launched until at last we approach the DC conditions. I would expect the initial high frequency electron movement to be at the surface, progressively getting deeper into the wire as the frequency falls, until near DC the entire wire carries the current. This propagation into the wire is by another slow EM wave which travels radially inwards.
If there is another wire nearby, then there is increased capacitance, so the electrons store their energy at a lower potential ie more spaced out. Now we are seeing a transverse component of electric field.
For a case where we have two wires forming a circuit, a battery and a switch, the initial impulse starts not from the battery but from the switch. I visualise that we have waves starting from each switch terminal and having opposite phase. These then travel around and around the circuit in opposite directions until Ohmic losses absorb them.
The EM radiation from a short wire terminated with resistance is broadside to the wire. This supports the view that the acceleration of the electrons is longitudinal.

 

[Delta2]

Because they don´ t depend on whether the charge carriers in wire are electrons, holes or heavy ions?

I think the speed of the waves doesn't depend on the exact nature of the charge carriers as long as the geometry of the transmission line remains the same (and ofcourse any dielectrics or magnetic permeability materials remain the same).

EDIT : I think after all that the charge carriers affect the parameter R of the transmission line, that is the ohmic resistance per unit length, which in turn affects the speed of waves. I had in my mind the lossless transmission line when I wrote the first paragraph if this post.

 

[Byron Forbes]

I think that your actual question is where that E-field comes from? Is it due simply to Coulomb repulsion or is it due to waves outside the wire?

Exactly!

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

I am not even sure what the source of this EM wave is!

If the wave is a product of electron movement in the first place, then surely if an electron moves near another, then it's electric field will have a greater, if not absolute effect, on the nearby electron, since any effect of an EM wave is the product of the initial electron's movement in the first place.

I will now reply to an earlier post that has relevance here.

 

[Byron Forbes]

It sounds like the OP is visualizing the EM wavefront to be analogous to a sound wavefront. Sound propagates only via particle collisions. But when an electron moves, its field changes with infinite extent and the change propagates at speed c in a vacuum. So when the first electron moves, that pushes all the other electrons in the wire (after propagating the EM field), not just the ones immediately in front. That makes electrons unlike gaseous neutral particles.

What you have stated about electrons and their field (to infinity) holds true in both circumstances.

In either case, conductor or particle, you have electrons interspersed with nuclei (protons) which greatly neutralises everything at a distance rendering the infinite reach of fields as negligible. The only thing worth considering is the nearby particles i.e. the ones with no other particles between them.

Again, I see the idea of the initial signal "wavefront" as a longitudinal wave through the electrons.

 

[Byron Forbes]

Yes he does, he's clearly refers to electrons

Let me expand.

The only reason I even mentioned this was to avoid the situation where I'm looking at an electron yet to move, but if it was more than halfway around the wire from the terminal I was talking about then it would have already been effected by the other terminal. It was also an attempt to show that the electric field is not immediately set up all around the wire instantly when the PS is turned on.

To expand, at the PS we have an E field acting across the wiring that's within the PS. So when the PS is turned on, it pushed electrons out of one terminal, therefore at the other terminal we have an electron vacuum. Since the electron pressure in the wire at this other terminal is now greater than at the terminal, electrons flow into it.

So we now have 2 signals traveling from both terminals that will meet at the halfway point of the wire.

 

[fluidistic]

https://www.bpa.gov/news/newsroom/Pages/Hitch-a-slow-ride-on-the-Electron-Express.aspx

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).

 

[Byron Forbes]

 

[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.