Electron Group Waves & Electromagnetic Waves, energy delivery in a wire

[mgladden2]

Hi all,

I still can't fully understand why electrons only drift in a copper wire DC circuit. The basic explanation I've been given is that electromagnetic waves carry the energy and move at roughly half the speed of light in copper, while individual electrons only drift along as the medium. My question becomes, how frequent are the electromagnetic waves? Why don't they have a frequency equal to about half the speed of light in copper, thereby causing the electrons to move just as rapidly. What scale even measures electromagnetic wave frequency in copper wire?

If your response is conjecture, please state as much. Thank you!

Here's some of what I've read, followed by some other specific points at which I'm confused:

1) The idea of current moving from positive to negative is an old convention which does not in any way correspond to what actually happens in an average copper wire DC circuit. Current actually moves from negative to positive in these circuits. The convention was setup by Ben Franklin and was kept because it was too much trouble to change years worth of formulas. I'm fine with this, but felt it important to mention because many explanations of energy transfer in DC circuits state that energy moves from positive to negative.

2) A DC power source forces electrons to "jump" from the source into the negative end of a copper wire in a closed circuit, while simultaneously "pulling" electrons out of the positive end of the circuit. Is this correct? Or does the source only "push" from the negative end and "catch" at the positive end? If it is correct, it sure messes up the analogy of a row of pool balls being hit at one end. It also adds confusion to the next few entries.

3) Copper wire is full of loose electrons (about one loose electron per atom), typically called the "charge sea", so when a circuit is first completed, the first group of electrons to "jump" from the DC source into the negative end of the circuit cause an electron group wave to begin propagating down the wire at about half the speed of light. As this electron group wave propagates, an interdependent electromagnetic wave is forming around the wire, causing the trailing electrons to "line up" instead of flitting about randomly. The electromagnetic wave exists because of the electron group wave, and at the same time it causes the electron group wave. (brain bender, but I can understand the interdependence).

This is where my confusion sets in. What is the interval of time between the first electromagnetic wave (and corresponding electron group wave) and the second one? Or "how far apart are the electromagnetic waves in a DC circuit?" I thought DC was by definition 0hz, but I think this must be a different scale we're talking about. One that measures electromagnetic wavelengths in wire versus voltage/current amplitude oscillations.

Also, if a DC source both "pushes" and "pulls", then what happens when we first power up a circuit? Is an electromagnetic wave propagating from positive to negative while another wave is propagating from negative to positive? Do the two meet half-way?

And finally, when everyone says "energy is carried in a wire by the electromagnetic wave" aren't we splitting hairs if that wave is interdependent on an electron group wave? Couldn't we just as easily say the increasing density of electrons in the propagating electron group wave is what delivers the energy to the load? Does anyone know whether the density of an electron group wave decreases after it passes through a load? Surely the strength of an electromagnetic wave must decrease after it passes through a load. Some joules must be removed and converted into heat or kinetic motion.

Thanks in advance.

Mark

Edit:

I found a website which suggests the frequency of electromagnetic waves in an AC circuit is the same as the frequency of the electric current. This would imply that every 1/60th of a second a new electromagnetic wave-peak and a corresponding electron group wave form around / enter into the wire at a power station, and then travel along the wire at about half the speed of light (for copper). The electrons would therefore only be forced to make their tiny "jump" to the next incremental position along the wire every 1/60th of a second, and they would not necessarily move in a clean, orderly fashion due to collisions, lattice impurities, etc, further slowing their forward progress. Can anyone confirm these ideas or relate them to my above questions?

http://www.nationmaster.com/encyclopedia/Electromagnetic-waves

When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current.

When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor.

 

[ZapperZ]

I think you are forgetting that in the Drude model, the free electrons are considered to be in an ideal gas. It means that they also collide with each other at ordinary temperatures and so, have a mean free path. When a potential is applied to such a system, even though there is a constant direction of force, the random collisions will still continue and therefore, aren't in the same situation as an electron by itself in an external field.

A solid state physics text typically covers this in great detail, usually in one of the earlier chapters.

Zz.

 

[mgladden2]

Thank you, Zz. I will see if I can find some online articles covering solid state physics. I would love to learn more about electron group waves and electromagnetic wave propagation in copper wire DC circuits. The common explanation of how electricity works in copper wire circuits is so utterly wrong that it has inspired me to want to learn more about it. I find that even well educated scientists commonly think electrons zip along at near the speed of light inside wires and cause light bulbs to glow by passing through thin filaments.

 

[Dale]

I find that even well educated scientists commonly think electrons zip along at near the speed of light inside wires

Really, I would be very surprised to find that. Even a site as basic as HyperPhysics has a good http://hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html#c3" page. If you go to that page and plug in 0.5 amps you get a drift velocity of 4 cm/hour. This would be a typical drift velocity supplying a 60W bulb on a 120V residential circuit with 12 gauge copper wiring.

What is the interval of time between the first electromagnetic wave (and corresponding electron group wave) and the second one? Or "how far apart are the electromagnetic waves in a DC circuit?"

I am having some trouble following your question. There are no electromagnetic waves in a DC circuit.

I would think that any transient waves that occur when you close a switch would emanate from the switch and not from either terminal of a power source.

 

[mgladden2]

I am having some trouble following your question. There are no electromagnetic waves in a DC circuit.

I would think that any transient waves that occur when you close a switch would emanate from the switch and not from either terminal of a power source.

Thank you for responding. It would certainly clarify things for me if there were no waves in a DC circuit other than maybe a transient wave when it is first switched on or connected to a power source. The problem is, everything I've read states that the electrons themselves are not carrying the energy nor doing the work. I've read two threads, one in which a person states that it is the group wave velocity of electrons that carries the energy. Another sums it up at the end of a long thread with "wires are hoses for electromagnetism".

http://amasci.com/miscon/ener1.txt

> ELECTRIC ENERGY IS NOT CARRIED BY INDIVIDUAL ELECTRONS
> Some books teach that, in a simple battery/bulb circuit, the
> electrons deliver energy to the bulb, and then they come back empty
> and need to be re-filled with energy by the battery. Some books
> give an analogy with a circular train track full of freight cars
> waiting to be filled. This is wrong. The energy in electric
> circuits is not carried by individual electrons, it is carried by
> the circuit as a whole.

Furthermore he writes:

I intended to communicate a simple idea: individual electrons in a
circuit do not behave as "energy buckets." When electrical energy
propagates from source to load, INDIVIDUAL electrons themselves DO NOT
move all the way from source to load. Instead, a battery injects
electromagnetic energy into one spot in a circuit and the EM energy
propagates among the population of electrons at the speed of light, while
the individual electrons themselves only drift very slowly at low cm/sec
velocities.

Another thread mentions the group wave velocity of electrons:

http://answers.yahoo.com/question/index?qid=20080821091120AAFvPY3

But the energy to light a bulb does not come from the electron drift, it comes from the group wave velocity of the electrons. And the wave velocity does in fact travel at light speed. Recognize that light speed in anything but a vacuum will be less than the traditiional C ~ 299E6 mps we typically associate with light speed.

The group wave velocity can be likened to the movement of ripples on a pond. The free electrons are the molecules of the water that, as a group, form the ripples. And it's the ripples, the electron group wave, that carries the energy used in a light bulb.

 

[Dale]

Another sums it up at the end of a long thread with "wires are hoses for electromagnetism".

That is a reasonable analogy. It is reasonable to think of electricity as an incompressible fluid. The analogy for pressure is voltage, and the analogy for current is (volume) flow. In a fluid power is pressure drop times flow, in a circuit power is voltage drop times current. The analogies go on from there, so it is useful.

But the energy to light a bulb does not come from the electron drift, it comes from the group wave velocity of the electrons.

I have a fundamental problem with this statement. The units are wrong. Energy does not have units of velocity, so energy can not come from a wave's velocity.

I'm not exactly sure what you are trying to say here. The energy in a circuit doesn't come from the speed of light any more than the energy in a pipe comes from the speed of sound. The energy in a circuit comes from the battery just like the energy in a pipe comes from the pump. When you open or close a switch the transient propagates through the circuit at the speed of light, just like when you open or close a valve the pressure propagates through the pipe at the speed of sound.

 

[mgladden2]

The energy in a circuit doesn't come from the speed of light any more than the energy in a pipe comes from the speed of sound. The energy in a circuit comes from the battery just like the energy in a pipe comes from the pump.

Hi Dale. Thank you for continuing to respond with insight. It makes sense that a battery supplies energy, but that energy must continue to propagate through the circuit. How does energy continue to propagate to a battery once the circuit has been formed? I always thought the electrons themselves carried the energy, and sort of "dumped" it at the load, but that appears to be wrong. The more I research, the more I read about the electric field which exists in a closed circuit. I have read that it is the electric field itself which transports energy to a load. How does energy move in an electric / electromagnetic field? Wouldn't it move in the form of electromagnetic waves?

What if we had hypothetical enormous circuit, say around the entire Earth with a really strong battery at one end and a light bulb at the other? (please disregard heating/capacitance or other reasons why this might be impossible and look at it for the sake of the concept which should apply to smaller circuits). If you were able to instantly switch it on, surely it would take some tiny but measurable time for the bulb to light up. What would be happening in the wire during that tiny amount of time? Would there be a wavefront moving through the wire as electrons were pushing their neighbors forward one "notch"? Would there be a corresponding electromagnetic field with a wavefront forming along the wire? Would it emerge from both the positive and negative ends to meet in the center, or would it only move from the negative end, to the bulb, and back around to the positive end?

The more I read, the more I'm finding the concept of slow electron drift understandable. The two reasons I can understand it are: 1) that a wire is like a HUGE pipe, full of an immense number of free electrons in the "charge sea", whereas most sources are pumping a comparatively small number of electrons into the pipe/wire. If a wire were so small that a cross section was composed of say 100 copper atoms, and you were constantly pumping 100 electrons into the wire, then the current speed might be the same as the "half the speed of light" you commonly hear as the speed of energy transfer or signal propagation in copper. And 2) that electrons don't move in a straight line in copper, but rather zig-zag around and collide with molecules, thereby further slowing their motion. Does that sound right?

 

[Dale]

Hi Dale. Thank you for continuing to respond with insight. It makes sense that a battery supplies energy, but that energy must continue to propagate through the circuit. How does energy continue to propagate to a battery once the circuit has been formed? I always thought the electrons themselves carried the energy, and sort of "dumped" it at the load, but that appears to be wrong. The more I research, the more I read about the electric field which exists in a closed circuit. I have read that it is the electric field itself which transports energy to a load. How does energy move in an electric / electromagnetic field? Wouldn't it move in the form of electromagnetic waves?

Think about this a little. In a DC circuit there are no EM waves and yet there is energy transfer. Therefore the http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html" even in the static (non-radiating) case.

What if we had hypothetical enormous circuit, say around the entire Earth with a really strong battery at one end and a light bulb at the other? (please disregard heating/capacitance or other reasons why this might be impossible and look at it for the sake of the concept which should apply to smaller circuits). If you were able to instantly switch it on, surely it would take some tiny but measurable time for the bulb to light up. What would be happening in the wire during that tiny amount of time? Would there be a wavefront moving through the wire as electrons were pushing their neighbors forward one "notch"? Would there be a corresponding electromagnetic field with a wavefront forming along the wire? Would it emerge from both the positive and negative ends to meet in the center, or would it only move from the negative end, to the bulb, and back around to the positive end?

I am pretty sure (say 90% sure) that it would emerge from the switch and propagate in both directions around the circuit.

The more I read, the more I'm finding the concept of slow electron drift understandable. The two reasons I can understand it are: 1) that a wire is like a HUGE pipe, full of an immense number of free electrons in the "charge sea", whereas most sources are pumping a comparatively small number of electrons into the pipe/wire. If a wire were so small that a cross section was composed of say 100 copper atoms, and you were constantly pumping 100 electrons into the wire, then the current speed might be the same as the "half the speed of light" you commonly hear as the speed of energy transfer or signal propagation in copper. And 2) that electrons don't move in a straight line in copper, but rather zig-zag around and collide with molecules, thereby further slowing their motion. Does that sound right?

Theoretically yes, but practically this would require such huge voltages and generate such an enormous amount of heat that you would vaporize your conductor.

 

[mgladden2]

Hi Dale,

Thanks for the replies. I found a link on that same page you sent that has another interesting statement:

For electromagnetic waves, both the electric and magnetic fields play a role in the transport of energy. This power is expressed in terms of the Poynting vector.

Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric and magnetic fields.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html#c2

That means in a wire carrying current, you should have a specific energy density for the electric and magnetic fields. When the current is first applied in my previous example of a huge circuit, you would then have a wavefront, which we both believe would move from both ends of the switch and radiate along the wire until it reached the opposing wavefront, where the field lines would connect (it would be great to somehow verify this). Once established, it sounds like the electric and magnetic fields would have a constant density, which would slowly decrease over time in a batter/load setup.

What was confusing me before is I kept thinking "but once a group of electrons moves into the wire from the battery, how soon does the next group move in?" I didn't realize that it's just the rate of current flow, and the reason the current moves so slow is that 12 gauge wire is like a HUGE pipe with an enormous amount of free electrons in the charge sea, whereas even at 20amps, you are only moving in a relatively smaller number of electrons, like a tiny pump feeding a gigantic pipe already full of uncompressable water.

With regards to the tiny wire idea, I'm confused when you say you would need a huge voltage. I'm under the impression that current moves faster through thinner wire, so even at 12 volts, wouldn't the current be incredibly fast if the wire only had 100 atoms per cross section? Let's say it was a perfect superconductor, rather than copper, to avoid heat loss issues. I now understand that the rate at which electrons would enter the wire is just whatever your current is, but I'm curious how fast can current move? Is there a real-world upper limit?

This whole idea that most of the every-day currents we encounter in our electronic devices are really moving at a snails pace seems strange, but I do now somewhat understand it. The energy moves at near the speed of light because the wire is already packed full of free electrons, but the electrons themselves only move slowly because the wire/pipe is so big and because imperfections in the lattice structure result in collisions and non-linear paths through the wire.

Interestingly, my brother-in-law who worked at Intel for years just wrote this in an email exchange:

the last architecture intel was working on before i left was so small (the line widths were about enough to accommodate one electron!) that the "wiggling" of a group of electrons could cause the copper line to actually jump out of its dielectric surround and cause shorts. they fixed this by creating silicon "tie-downs" that went across the top of the line every few microns or so.

This link also verifies the idea that work done by an electric circuit is performed "against the Electric field":

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/volcon.html#c1

 

[nuby]

From what I understand there are three (wave) velocities within a circuit. Electron drift velocity.. slow.. the linear speed of electrons down the circuit. The fermi velocity (about 1/2 c) which is the speed of the conductive electrons bouncing around atoms, and the signal velocity (not 100 percent sure) is the linear velocity which electrons propagate their charge down the conductor.

 

[Dale]

With regards to the tiny wire idea, I'm confused when you say you would need a huge voltage.

There are about 8.5E28 free electrons/m³ in copper, so that gives a cross-sectional area of about 5E-20 m² for a "100 electron" wire. Neglecting relativistic effects, to get a http://hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html#c3" of 340 MOhm, so 102 mA would require 35 MV!

Also, the 2 EA/m² you are talking about is about a billion times higher than the highest current density that even http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/scex2.html" can handle.