Whether the speed of alternative/direct current is faster than light?

[ghwellsjr]

But how to explain electric energy can be sent to users miles away by copper wires whose frequency is very low(60Hz or 50Hz) in power industry?

What has the frequency got to do with energy transmission? It can be done at DC, too.

 

[Q-reeus]

If you look at the text just above equation 3-77 of your book it states:
Where then subsequently n is used in that equation. This n is also used in equation 3-79. So all I can deduct from that book is that “the total electron density” must be used.

Now allow me to be very confused indeed.

Your continued confusion is in seeing the *Drude equivalent* expressions that Kittel, Blakemore above quoted, and Mehring in the uploaded article, use, while somehow missing the accompanying explanations that the *real* situation is quite different in detail, but divergent factors cancel out for overall result. For instance, did you read the part on p185 of Blakemore where he remarks "We can understand now that for a degenerate electron gas, the mean free time for only a small minority of the total electron population is significant. It has been remarked that Sommerfeld drew an important distinction between the large number of "free electrons" and the much smaller number of "conduction electrons"."? He goes on to explain some deficiencies in the Sommerfeld model, which for instance retained the Drude assumption of elastic scattering, whereas inelastic scattering applies. In many real metals the fermi surface is far from spherical, and density of states, effective mass, mfp, are all anisotropic quantities. But that all gets into details far from the OP's interest.

 

[Q-reeus]

...Do any of you have an insight on this related question: Why does tungston with only about 3.3 times the resistivity of copper get so hot...as in light bulbs...Is it mostly a function of the filament being so thin? I am wondering if there is something different in the conduction band energies of resisters that causes so much heat to be generated...
Thanks...

Naty1: Would say the sole reason tunsten is (still) used is owing to it's very high melting point and thus high retained mechanical strength at those elevated temperatures where emission of light is reasonably efficient. Push enough current through any resistance and it gets hot of course, but copper for instance would melt at dull red heat. A nice feature of the filament lamp is the current self-limiting owing to positive temperature coefficient of resistance. A less nice feature is the development of a hot spot owing to uneveness in the inevitable slow sublimation of the filament.

 

[Q-reeus]

Some intended edits for #27: factor 1/2 should have been 3/2. Also, at zero temperature there is no thermally excited 'intrinsic' unpaired electron population, and high conductivity there is entirely due to Fermi surface displacement by an applied E, coupled with a very long mft limited only by 'intrinsic' lattice defects. Thus it may be best to restate the two-track conduction process as superposition of a minor Drude type drift mechanism applying to the thermally generated population of unpaired electrons, and a major, essentially temperature independent vectored emission Fermi surface displacement mechanism at the heart of the Sommerfeld model.

My own interest in this area sprang from finding some very interesting results for certain current configurations owing to higher order relativistic effects - synchrotron radiation being an extreme example of relativistic harmonic generation. While for high power Magnetrons harmonic generation is considered objectionable as it robs power from the intended fundamental frequency output, in other situations it could be a plus. Even though for metallic conduction electrons moving at ~ 0.3% c, the very small first harmonic ~ 10^-5 times smaller than the fundamental, that could be useful in some configurations. Suspected though that in the stop-start scattering of room temperature regime, it might be entirely suppressed, and was never convinced that even in the ballistic regime of tiny dimension very pure metals at very low temperature, conduction electrons really behaved elecrodynamically identically to truly free electrons (such as in a cyclotron). Would love to know though.

 

[Q-reeus]

But how to explain electric energy can be sent to users miles away by copper wires whose frequency is very low(60Hz or 50Hz) in power industry?

Adding a bit to what ghwellsjr said in #31, found an online simulation that can help to get a feel for how 'throwing the switch' at one end of a DC line is initially a series of waves going back and forth - at c or less: http://users.ece.gatech.edu/~wrscott/applet_bounce/Reflect1.html

 

[Per Oni]

Your continued confusion is in seeing the *Drude equivalent* expressions that Kittel, Blakemore above quoted, and Mehring in the uploaded article, use, while somehow missing the accompanying explanations that the *real* situation is quite different in detail, but divergent factors cancel out for overall result.

Since you now also quote Kittel, I take it that you fetched a copy from your local library. I am glad you at last agree with him. Please read chapter 6 very carefully and slowly. Middel of page 127:

In a free atom of sodium the valence electron is in a 3s state; in the metal this electron becomes a conduction electron. We speak of the 3s conduction band. A monovalent crystal which contains N atoms will have N conduction electrons and N positive ion core.

Tell me which letter, word, sentence in this quote supports your theory?
In fact answer me the same question regarding that whole chapter. And note that chapter is not about Drude it’s about Sommerfelt and more.

This is now becoming a bit comical, in #26 someone asked: Can anyone cite a recent reference that actually computes the drift speed for a copper wire?
You replied: “Can't right now think of any specific calcs available online, sorry.”
On the other hand there must be dozens of sites calculating a slow velocity in English alone, multiply that with about 100 or so for other languages then it looks like you cut a lonely single figure.

If you still want to answer me please stick to my questions regarding Kittel.

 

[ghwellsjr]

Adding a bit to what ghwellsjr said in #31, found an online simulation that can help to get a feel for how 'throwing the switch' at one end of a DC line is initially a series of waves going back and forth - at c or less: http://users.ece.gatech.edu/~wrscott/applet_bounce/Reflect1.html

That's a cute animation.

However, it's showing how not to build a transmission line, at least with the default parameters because it's unbalanced at both ends. If you click on the circuit diagram in the lower right corner, a dialog box will pop up allowing you to change the values of the resistors and impedance.

If the load resistance matches the characteristic impedance of the transmission line, then there will be no reflection at the load. If the source resistance matches the characteristic impedance of the transmission line, then there will be no reflection at the source. Since the default values of both resistances do not match the impedance, there are lots of reflections back and forth.

If you change the source resistance to 25 ohms, you will see one reflection at the load but none at the source.

If you change the load resistance to 25 ohms, you will see no reflections.

As long as the load resistance matches the line impedance, it won't matter what the source resistance is, as far as reflections go, because a mismatch there only makes a difference if there is also a mismatch at the load. However, it does reduce the actual voltage level and therefore the energy transferred if the source resistance is anything other than zero. The animation does not label the values of the voltages in the graphs so this is a little hard to see.

Also, the speed of propagation is always less than c.

 

[Q-reeus]

Since you now also quote Kittel, I take it that you fetched a copy from your local library...

No. I will admit to taking a certain liberty on the basis that a well known authority like Kittel would not be backing the Drude concept against Sommerfeld and ongoing more modern and detailed theory.

I am glad you at last agree with him.

Undoubtedly, but for sure he will not be agreeing with you.

Please read chapter 6 very carefully and slowly. Middel of page 127:
"In a free atom of sodium the valence electron is in a 3s state; in the metal this electron becomes a conduction electron. We speak of the 3s conduction band. A monovalent crystal which contains N atoms will have N conduction electrons and N positive ion core."
Tell me which letter, word, sentence in this quote supports your theory?

So Kittel uses the term conduction electron here and this somehow overthrows everything I have presented and quoted from!?

In fact answer me the same question regarding that whole chapter. And note that chapter is not about Drude it’s about Sommerfelt and more.

Why would I bother - you don't understand it, or more likely don't want to admit that what is really being said there fails to back your outdated notion of how it all works.

This is now becoming a bit comical, in #26 someone asked: Can anyone cite a recent reference that actually computes the drift speed for a copper wire?
You replied: “Can't right now think of any specific calcs available online, sorry.”
On the other hand there must be dozens of sites calculating a slow velocity in English alone, multiply that with about 100 or so for other languages then it looks like you cut a lonely single figure.

Suggested reasons for this dichotomy have been given previously. I've tried to be civil as possible with you, but clearly your aim is simply to be proved right no matter what.
Right here at PF there is at least one thread you should visit: https://www.physicsforums.com/showthread.php?t=121519
Still not convinced? Then try a read of section 1.4 at this online site: http://books.google.com.au/books?id...ook_result&ct=result&resnum=7&ved=0CE0Q6AEwBg
Need more again? If so sure that the Drude model you defend is correct, despite the above and everything previously posted, try posting in the appropriate section: https://www.physicsforums.com/forumdisplay.php?f=64. You can't accept what I have presented; fine, go see if the real pro's will back your ideas. I'm done arguing - this has gone on too long already and is off topic. Give it a rest, OK!

 

[Q-reeus]

That's a cute animation.

However, it's showing how not to build a transmission line, at least with the default parameters because it's unbalanced at both ends. If you click on the circuit diagram in the lower right corner, a dialog box will pop up allowing you to change the values of the resistors and impedance.
If the load resistance matches the characteristic impedance of the transmission line, then there will be no reflection at the load. If the source resistance matches the characteristic impedance of the transmission line, then there will be no reflection at the source. Since the default values of both resistances do not match the impedance, there are lots of reflections back and forth.
If you change the source resistance to 25 ohms, you will see one reflection at the load but none at the source.
If you change the load resistance to 25 ohms, you will see no reflections.
As long as the load resistance matches the line impedance, it won't matter what the source resistance is, as far as reflections go, because a mismatch there only makes a difference if there is also a mismatch at the load. However, it does reduce the actual voltage level and therefore the energy transferred if the source resistance is anything other than zero. The animation does not label the values of the voltages in the graphs so this is a little hard to see...

Yes I agree with everything you say there, but just note that typically for a DC load there is no thought of matching so reflections would be the expected general case. It was unfortunate that little explanation accompanied the animation, but have not so far come across a better one.

Also, the speed of propagation is always less than c.

For a practical transmission line with dielectric insulation yes. But a fully evacuated length of coax for instance will propagate at c - that is in accordance with TEM mode theory. Air filled line will be a whisker less. Can't recall offhand if slightly imperfect conductivity effects propagation velocity, but if so, throw in 'perfect conductivity' to the above.

 

[Per Oni]

Give it a rest, OK!

Rest assured in the knowledge that I will defend my point of view.

 

[ghwellsjr]

Also, the speed of propagation is always less than c.

For a practical transmission line with dielectric insulation yes. But a fully evacuated length of coax for instance will propagate at c - that is in accordance with TEM mode theory. Air filled line will be a whisker less. Can't recall offhand if slightly imperfect conductivity effects propagation velocity, but if so, throw in 'perfect conductivity' to the above.

I was mistaken. Thanks for pointing this out.

I was remembering the formula from one of my textbooks for the velocity of a signal in a transmission line:

v = 1 / √(LC)

and thinking that it was directly related to the characteristic impedance:

R0 = √(L/C)

but, of course, it's not.

Later on in the book, they have the formulas for C and L in a coax line and plugging them into the velocity formula yields:

v = 1 / √(με)

And, of course, for free space, με = 1 / c², so v = c.

 

[Q-reeus]

...Later on in the book, they have the formulas for C and L in a coax line and plugging them into the velocity formula yields:
v = 1 / √(με)
And, of course, for free space, με = 1 / c², so v = c.

Right on. If you can grab a copy of Foundations for Microwave Engineering - 1st ed'n, R.E.Collin, ch.8 'Periodic Structures and Filters' goes into how it is possible, without any use of dielectric, to modify coax with periodic radial fins so as to increase the effective value of C without appreciably effecting L. This is at the expense of introducing stop and pass bands, and having characteristic impedence Z₀ a periodic function of distance along the line, owing to backward waves coexisting with forward waves. It is entirely possible that C could be reduced rather than increased by incorporating series inductance into each fin that overpowered the capacitive part. Using v = 1 / √(LC) would seemingly then give a superluminal propagation speed v > c but that doesn't follow because there are now two v's - v_p and v_g (I'm reverting here to standard terminology for group velocity, rather than the v_s I had used earlier) - the line being now dispersive acts in part like hollow waveguide, despite the mode still being purely TEM. Always v_g < c, which is what really matters re 'superluminal' signals. [EDIT: Actually the formal value of v_g can exceed c in the anomalous dispersion region (e.g. weakly ionized plasma), which is a possibility in such a periodic structure. But this just refers to motion of the peak of a pulse, and the remarks made in #19 then apply]

 

[Naty1]

I wonder if the OP is still here...

The illustrative example I find helpful is picturing automobiles getting on a crowded highway...and others exiting miles away...each auto (electron) itself moves slowly but the effect (the wave) is almost instantaneous, perhaps approaching the speed of light, as a distant car exits the highway for each one entering...

 

[Obamon]

Maybe you are driving in a wrong direction. The speed of electric current has nothing to do with electrons which are too slow. It should be energy speed of the electromagnetic field in solid metals( See a paper "Energy transport in good conductors").

 

[Phrak]

To be precise, the OP asked about "the speed of alternative[sic] and direct current", in comparison--not how fast charge moves or how fast electrons move.

The disturbances in current propagate at about 75 to 95% c. The "speed" of current is another matter and is exactly zero.

 

[Q-reeus]

Maybe you are driving in a wrong direction. The speed of electric current has nothing to do with electrons which are too slow. It should be energy speed of the electromagnetic field in solid metals( See a paper "Energy transport in good conductors").

If you follow through the reasoning in that paper (actual title: Energy transport faster than light in Good Conductors), it is quickly found the author is conflating totally different phenomena. Very slow and *imaginary* propagation *through* a good conductor cannot sensibly be combined with the *longitudinal* energy flow *along* a conducting wire TL as he has done. Garbage in, garbage out.