A paradox about Drift Velocity

[Dadface]

The power expended in moving the electrons and delivered to the load (the 100W in your example above) are two different things. The output or load power delivered by the conductor is not the force on the charge carriers (electrons) x their drift velocity.

But its interesting that when you equate P=VI with I=nAve you do get a P=Fv type equation the full equation being P=N*Fv(see my post above).I know it seems odd.

 

[Per Oni]

The power expended in moving the electrons and delivered to the load (the 100W in your example above) are two different things. The output or load power delivered by the conductor is not the force on the charge carriers (electrons) x their drift velocity.

Correct for the case of real electrons.
However now use sweeties / ball bearings etc. in a tube instead of electrons and you will find that for 100W to be supplied with v= 0.006 m/s there’s a big force present on this medium.

I suppose the real difference is that electrons carry (are carriers of) electro magnetic fields. Any disturbance in these fields are propagated close to the speed of light, depending on what kind of cable and insulation.

 

[Dale]

I am a little puzzled why you reacted to my correct post and not to some of the previous wrong posts.

Thanks for the clarification as to your intent. I simply reacted to your post because the number you gave for stress was off by 11 orders of magnitude.

The suggestion in this thread is that the signal speed of current in a wire can be explained using the analogy of a tube of sweeties where one enters, side pushes all the adjacent sweeties so that the last one pops out of the tube at the far end. This picture is wrong for a number of reasons.

I wanted to show what the implications are, considering the forces involved transporting any average power that way, knowing that the medium (sweeties) travel at an extremely slow speed. Because that way since F=P/v, force and therefore pressure become very high indeed.

I think you are overreacting here. The analogy is adequate for its intended purpose which is to demonstrate that a low drift velocity is consistent with the observed fact that the lights come on as soon as we flip the switch. It is just an example used to help students get comfortable in an intuitive mechanical way with the idea that the drift velocity does not limit the propagation of the electrical current.

Also, the analogy is not so far from the truth. When you push one sweetie in on one end one pops out on the other end (conservation of charge). Moving the sweeties heats up the tube (resistance) and reduces the force that the last sweetie can push with (voltage drop). The last sweetie doesn't quite start moving instantaneously (finite speed of light). Etc.

As with all analogies it fails at some point, and it is good to point that out to students. In this case it fails to explain the stress of the EM field. But if we were to insist that all analogies be completely perfect in all situations then we could never use any analogies at all. The analogy is good (although I prefer the plumbing analogy to the sweeties one) and is useful to students in learning a challenging subject. It correctly addresses the OP's question which did not extend to EM stress or other topics outside of the proper scope of the analogy.

 

[Per Oni]

Thanks for the clarification as to your intent. I simply reacted to your post because the number you gave for stress was off by 11 orders of magnitude.

This amount of stress I calculated is correct for the case of sweeties in a tube. I wanted to indicate just how ridicules this analogy is in point of view of forces involved. And yes compared with real conduction its way way off, but that’s just the point I’m making. I don’t need a house rewire each time something like a hairdryer gets switched on.

As to your feeling that the plumbing theory it is sort of ok, some time ago I read an article (it could be wiki) which proposed 2 different theory’s of electrical conduction one based on plumbing and one following the theory of the Poynting vector. (Perhaps it has been removed?) If we don’t point out discrepancies eventually it will end up all the way up there.
Just reading some wiki pages I found this: http://en.wikipedia.org/wiki/Poynting_vector:

DC Power flow in a concentric cable

Application of Poynting's Theorem to a concentric cable carrying DC current leads to the correct power transfer equation P = VI, where V is the potential difference between the cable and ground, I is the current carried by the cable. This power flows through the surrounding dielectric, and not through the cable itself.[7]

However, it is also known that power cannot be radiated without accelerated charges, i.e. time varying currents. Since we are considering DC (time invariant) currents here, radiation is not possible. This has led to speculation that Poynting Vector may not represent the power flow in certain systems.[8][9

So it looks like there’s still some controversy.

There’s another aspect of electrical conduction theory I like to mention, namely: energy leaves the source at near light speed towards the surrounding dielectric. Therefore it follows that the source should receive a kickback in the opposite direction. Has anyone ever seen a paper dealing with that fact, or anyone any thoughts?

 

[akinokoe]

Here is the simple explanation. The switch-on time is not dependent on the drift velocity. After the circuit is switched on, the electric field is applied on the appliance immediately (the speed of the propagation of the field is about 1/10 of the speed of light). At the same time the electrons start to drift and thus current is formed. We can also say within the time of the length of the circuit divided by 1/10 of the speed of light, the drift velocity along the wire can reach the same value. The time that is consumed is not dependent on the drift velocity but the speed of the propagation of the electric field.

 

[azaharak]

To get an approximate idea of the order of drift velocity without much math,

charge of electron is roughly 10^-19C, so a one amp current in a wire corresponds to an exchange of 10^19 electrons per second, since these are the charge carriers.

A piece of matter that you hold in your hand has roughly 10^23 atoms, (via avogradro).

so you figure you have roughly 10^23 valence electrons (via atoms), but you only need to move 10^19 of them every second.

So they must move on average 10^-4 m/s.

Quick approximation, you'll do better by knowing the current, current density, & concentration of valance electrons.Specifically, the drift velocity doesn't mean that's how fast the signal propagates. If I move an electron on one side of the wire, that coulomb field (disturbance) propagates at the speed of light. In practice the electron at one end of a wire never reaches the other end (according to this classical drift velocity idea), it would take an awfully long time. However the signal particularly in Ac propagates at "near" (see last line) the speed of light.

Even with :slowed: light in a medium, the light still travels at C, its just the light gets absorbed and re -emitted and this takes a certain amount of time which delays the light.

the light however always travels at C, but we speak of the speed of the light in the medium to include these absorption and emission times.

Another thing to keep in mind, the coulomb disturbance mentioned above is mediated by light itself, so it will feel the effects of the delay time, all relative to permittivity and permeability.

 

[PhilDSP]

Just reading some wiki pages I found this: http://en.wikipedia.org/wiki/Poynting_vector:

So it looks like there’s still some controversy.

There’s another aspect of electrical conduction theory I like to mention, namely: energy leaves the source at near light speed towards the surrounding dielectric. Therefore it follows that the source should receive a kickback in the opposite direction. Has anyone ever seen a paper dealing with that fact, or anyone any thoughts?

But a so-called "DC current" is not time-invariant. At the molecular level the electrons are making short hops as they jump from place to place. There is a constant exchange of convection current, where the electrons carry the current, and displacement current where the "medium" carries the current or energy.

 

[Gokul43201]

The electrons themselves move at a low average drift velocity, but the current in the wire moves at close to the speed of light.

This is incorrect. The current is nothing but the flow of electrons, and is in fact quite directly related to the drift velocity. It is the electric field that propagates along the wire at the speed of light.

Imagine electrons traveling in a circuit like when I push a very long pencil. I push on one side of the pencil, and the other side moves (almost instantaneously)! The current, then, is not determined by how fast I can push the pencil, but by how much of the pencil moves past a certain point within a certain amount of time.

All of the electrons within the wire start moving almost instantly after the circuit is switched on. This is very much like how all of my pencil starts moving almost instantly after I push it.

Imagine a cardboard tube full of sweets. If you push in another sweet at one end another drops out of the opposite end, no matter how long the tube is. That shows that the sweet put in only travels a couple of millimetres yet its action can be seen instantly at the other end of the tube which could be a metre away! How is that?

I hate these analogies, not because they miss little details about propagation speeds and "instantaneous" effects, but because they fundamentally mislead in terms of explaining the effect. One would gather from these analogies, that the current is driven primarily by electron-electron interactions (or collisions), but that couldn't be further from the truth. The current is generated as a response of all* the free electrons in the wire to the applied field, and any analogy ought to make some attempt at conveying that basic idea.

It is the fault of this poor shock-wave analogy that, I believe, leads to statements about current traveling at close to c. Or statements like the following, extracted from above: "The current, then, is not determined by how fast I can push the pencil, but by how much of the pencil moves past a certain point within a certain amount of time." How fast I can push a pencil is exactly the same thing as how much of the pencil moves past a fixed point over some time - that is essentially the definition of "fast" (or speed). But by restricting oneself to the failing analogy, one has to use rather weird definitions.

A better analogy might be holding a string of beads by one end and letting go. All the beads travel downwards in response to the same external field (gravitational, in this case), but occasionally feel weak tugs from other beads (electron-electron interactions) and from the air around them (electron-phonon and electron-impurity interactions).

*Ignoring Fermi distributions - I'm using "all" to mean throughout the length of the wire.

 

[mheslep]

A better analogy might be holding a string of beads by one end and letting go. All the beads travel downwards in response to the same external field (gravitational, in this case), but occasionally feel weak tugs from other beads (electron-electron interactions) and from the air around them (electron-phonon and electron-impurity interactions).

Yes, yes, that's a much better analogy, thanks. I think it still misses slightly in that, unlike a gravitation field and beads, the availability of the conduction band electrons influence the degree to which the EM field propagates (though having ~no influence on the speed of the EM). Sound right?

 

[Gokul43201]

Yes, it misses what I think are (relatively) smaller details (like the dielectric function that you mention), but that's inevitable with any analogy. Still, I like it a lot better than the analogy using the pencil (or the horizontal line of balls/sweets) which serves little or no pedagogical value, and IMO, is more likely to propagate misconceptions than clarify them.