Electron Migration

The Classic Column on 7/19/00 is from 7/22/94:

How long does it take for electricity to travel from the generator where it is produced to the light bulb at my house? – Roberto Chevres

Cecil replies:

[snip]
Incidentally, while the juice as a whole moves pretty fast, the individual electrons don’t. This being alternating current, they dance frantically to and fro and never get anywhere. Just like thee and me.


No. No. No.

Despite what they may have told you in high school physics, electrons do NOT migrate down the wire from the generating plant to your house and into your toaster, and would not do so even if the supply were DC rather than AC.

That is (putting aside the quantum mechanics question about whether they are physical entities), electrons do not flow down wires, jumping like cattle-prodded frogs from one atom to the next.

Rather, it’s the ENERGY that travels down the wire, like the desk toy with the steel balls hanging from wires, where you pull back the ball on one end, it whacks the next ball, and the energy is transmitted down the line of balls to the last one, which flies out. The other balls hardly move at all.

Remember how as a kid you would pull a clothes line taut and tap it to send a “loop” down the line, to bounce back and forth. The atoms in the line don’t move horizontally, but only waggle as the energy wave travels.

It’s like a wave in the ocean. It’s not particular molecules of water moving along, but energy transmitted from one molecule to the next. A particular molecule of water moves in a closed curve (roughly oval) and ends up where it started.

Incidentally, AC or DC would make no difference. Since electric energy moves down a wire at a considerable fraction of the speed of light in a vacuum, if a particular electron is imagined (contrary to fact) to move down the wire, at the AC frequency of 60 Hz, it would have plenty of time to zip from the generating station to your house and back before the polarity changed.

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Cecil’s column can be found on-line at this link:

How long does it take electricity to travel from the generator to my house? (22-Jul-1994)
K43, it seems to me that you are agreeing with Cecil Adams, who says in the sentence you quote that the electrons don’t move.

Arnold, my interpretation of Cecil’s column is that he’s saying, “electrons don’t move (much) along the wire because it’s an AC current.” The implication is that if we were talking a DC current, electrons would move a measurable distance. This is what K43 disagrees with.

And, with that intro: Are you sure 'bout your contention, K43? This site, for example, claims that electrons in a typical lamp cord move along the wire at a rate of 8.4 cm/hour. Note this is not the speed of light (or thereabouts), so your comment about electrons having time enough “to zip from the generating station to your house and back before the polarity changed” is not correct.

And, incidentally, why wouldn’t electrons travel down the wire? They’re charged particles, and I don’t think it’s that difficult for them to move around in a metal matrix. If your contention is that they stay in the same place, what keeps them there?

Electrons do move down the wire.

There is a unit of electic current called the AMP it is a measure of the amount of electric charge that moves past a cross section of the wire per second. This charge in metal wires is carried by electrons.

1 Amp of current can be made up of a few electons moving fast or many electrons moving slow.

In metal wires it is many electrons moving slow.

This is the point made in the SD column. The other point is that it is AC and so they change direction frequently.

When you turn on the light switch the electrons start to move. The electrons start to move near the switch and the starting to move wave front moves down the wire at about the speed of light.

[QUOTE]
*In response to post by K43 *
The Classic Column on 7/19/00 is from 7/22/94
Let me start by saying that as a physics teacher, I take offense to your remark about high school physics … perhaps you would never have said it if you actually understood the topic being discussed.

I will now pick apart your post piece by piece (The Straight Dope on the topic then follows):

YOU SAID:
Despite what they may have told you in high school physics, electrons do NOT migrate down the wire from the generating plant to your house and into your toaster, and would not do so even if the supply were DC rather than AC.

I SAY:
It is true that with AC, electrons do not get very far in any half-cycle, and then are put back to essentially where they started in the next half-cycle. In DC however, there is a net flow of electrons. For typical currents in typical wires, this “Drift Velocity” (as it is called) is very slow: about a millimeter per second or slower for the wire attached to your toaster, if your toaster was plugged into a 120 V DC source. Do not confuse the speed of electrons moving with the speed of the electrical signal: the latter is quite fast (details below).

YOU SAID:
That is (putting aside the quantum mechanics question about whether they are physical entities), electrons do not flow down wires, jumping like cattle-prodded frogs from one atom to the next.

I SAY:
I don’t have a clue what you are talking about here (there is no “question about whether they are physical entities” - to make sure, I even contacted a professor of modern physics, who agrees that you seem not to have a clue … perhaps you could clarify what you mean here. Again with the electrons moving though: when we speak of current, we measure it in “Amps” - where an amp is a unit of charge flowing per second; current is charge in motion. To have current and no charge in motion is a contradiction.

YOU SAID:
Rather, it’s the ENERGY that travels down the wire, like the desk toy with the steel balls hanging from wires, where you pull back the ball on one end, it whacks the next ball, and the energy is transmitted down the line of balls to the last one, which flies out. The other balls hardly move at all.

I SAY:
This is a fantastic analogy, but one that does not apply here. This would relate more to a spark jumping from a wire - the electrons at the end of the wire are “kicked out” and move significantly, though other electrons in the wire barely move.

YOU SAID:
Remember how as a kid you would pull a clothes line taut and tap it to send a “loop” down the line, to bounce back and forth. The atoms in the line don’t move horizontally, but only waggle as the energy wave travels.

I SAY:
What you are describing is wave propagation. Electricity flowing down a line is not purely a wave phenomenon.

YOU SAID:
It’s like a wave in the ocean. It’s not particular molecules of water moving along, but energy transmitted from one molecule to the next. A particular molecule of water moves in a closed curve (roughly oval) and ends up where it started.

I SAY:
This is a good analogy for electron movement in AC, but not DC … DC electrons would flow, much as the water molecules do flow in a river or stream.

YOU SAID:
Incidentally, AC or DC would make no difference. Since electric energy moves down a wire at a considerable fraction of the speed of light in a vacuum, if a particular electron is imagined (contrary to fact) to move down the wire, at the AC frequency of 60 Hz, it would have plenty of time to zip from the generating station to your house and back before the polarity changed.

I SAY:
Again, as discussed above there Is a difference. Electrons typically travel relatively slowly within conductors as mentioned above, and so would not go to your house and back before the polarity changed.

The Straight Dope:
Here it goes … electrons themselves travel quite slowly within a conductor that has a current in it. The original question was, however … “How long does it take electricity to travel from the generator to my house?” I think I can do a reasonable job answering this:

The answer is: that it depends on many factors and is quite complicated. However, I am fortunate to have a summer job with a company who builds computer systems that are designed to simulate the intricate workings of a power grid (see http://www.rtds.com if you like). With a little help, I set up a simple simulation of a generator hooked up to 15 km of typical transmission line, and monitored the voltage at the end. According to this simulation, after closing a switch at the generator end, the voltage appeared at the far end about 55 microseconds later, which would give this electrical signal a speed of about 2.73E8 m/s, or about 91% of the speed of light. Knowing this, and the length of conductor that separates your toaster to the generator, you should be able to get a ball-park answer.

So, how does that electroplating stuff work?

The physics teacher was getting closer to the right answers.
Here’s my attempt to further clarify things. Hope I don’t muddle them too much in the process.

(1) Electrons do migrate down the wires. For every ampere of current you have Avogadro’s number (about 6 with twenty two zeroes after it) of electrons per second flowing by any point in the wire. That’s a sixty thousand billion billion electrons per second. Sounds like a lot, but electrons are so tiny, they’re just barely crawling by,
somewhat slower than a turtle’s crawl.

(2) The POWER does go down the wires at near the speed of light. In most areas those big overhead towers carry the electricity most of the way between your and the power plant. The speed of light in wires in free air is quite close to the speed of light. There are abrupt delays going thru the power transformers-- they can introduce several thousandths of a second of delay.

(3) Individual electrons don’t run all the way from the power plant to your house. There are usually at least 3 transformers between you and the power plant. Transformers don’t pass electrons, they use magnetic coupling to transfer the energy, no actual electrons can cross over.
So the electrons coming out your wall outlet only loop around from you out to the nearest distribution transformer, usually less than a block away.

(4) Other complications-- most utilities are hooked up to the national power grid, so your power doesnt strictly come from the local power station, small amounts come from all over the country. There are many delays in this network,
as there are scads of transformers, AC/DC inverters, even pumped storage facilities.

(5) Most wall power is 60 cycle per second AC. Since the electrons are just crawling, and reversing direction every 120’th of a second, individual electrons just end up wiggling back and forth a few millimeters at most.

(6) Then again, the power in your car is mostly DC. When you turn the key to start your car, about 100 to 400 amps of DC current flows from your car battery to the starter motor. That is a lot of current, but even then the individual electrons don’t move at more than a walking pace.

(7) If you live on an island, your power probably comes from the mainland thru an underwater cable. The insulation on the cable has something called a “dielectric constant”, which slows down the speed at which the power flows down the cable. So your power can take up to twice as long to get to you (still just a few thousandths of a second at most).

Hope this helps clarify things a trice. Everybody was at least partially right in some sense.

*In response to post by grg *

I agree with most of what you said, but you need to be corrected on one important point, and then I will take another stab at further clarification.

In your first point, you said that “For every ampere of current you have Avogadro’s number (about 6 with twenty two zeroes after it) of electrons per second” This is not correct: an amp is actually a Coulomb of charge flowing past a point per second, where one Coulomb is about equal to 6.24E18 electrons: a huge number to be sure, but almost 10 000 times smaller than Avogadro’s number.

A problem in this discussion seems to be that there is no clear meaning to the phrase “speed of electricity” - I think that this is because “electricity” is not a measurable quantity, but rather the general topic of interest here (there are of course many electric quantities that are themselves measurable). Asking what the speed of electricity is is kind of like asking what the speed of optics is.

Having said this, there are two separate electric quantities that have come up: the speed of the electrons themselves, and the speed of the electric signal. As has been mentioned already, electrons themselves typically travel very slowly when confined to a solid conductor such as a wire. It is quite easy to calculate this drift velocity. If you are so inclined to learn how, read the last paragraph of this post; if not, skip it. As for the speed of the signal, yes, this is very fast - nearly the speed of light.

To help distinguish between these two speeds, consider the following analogy: Take a meter stick laying flat on a table at rest, then push one end of it slowly so that it moves in the direction it is pointing. If we talk about atoms (molecules etc), then realize that the speed of these atoms as they move across the table is very slow BUT, the speed of the signal generated within it is very fast. Think about it … you (the “generator”) only pushed the atoms at your end of the stick, yet the atoms at the other end of the stick also responded, due to the interaction of the atoms within the stick. I hope this helps.

Here’s the calculation: Let’s assume a typical toaster-type cylindrical copper wire of cross-sectional radius 1 mm with a steady current of 10A. This means that the wire has 10A = 6.24E19 electrons flowing past a point each second. Copper atoms are said to be “monovalent” - they each contribute one electron to the flow of this current. This means that a section of wire containing 6.24E19 copper atoms has the electrons from the back end of the section reaching the front end in exactly one second: find the length of this section of wire, and convert it to a speed (of the electrons). Here’s how: copper has atomic mass 63.5 = 0.0635 kg/mol and we have
6.24E19 atoms / (6.02E23 atoms/mol) = 1.04E-4 mol
This means that the mass of our wire segment is
1.04E-4 mol * 0.0635 kg/mol = 6.58E-6 kg
Since copper has a density of 8900 kg/m^3, our segment must have a volume of 6.58E-6 kg / 8900 kg/m^3 = 7.4E-10 m^3
Since the segment has a volume calculated by V=(Pi)r^2L, we can find the length of the wire segment to be 2.4E-4 m. **
This means that the speed of these electrons would be 0.24 millimeters per second.** Of course, this is only for the wire attached to your toaster. You can do similar calculations for whatever kind of wire you want. Overhead transmission lines are much thicker, have much more current, and are usually aluminum reinforced with a steel core) Note also that the “steady current” this calculation applies to would necessarily by DC - I think we have already clarified the DC vs AC issue.

I see a slight disjunction here.

I don’t. Mr. Physics is using the ratio of the number of electrons in a Coulomb of charge to the number of atoms in a mole (Avagadro’s number) to determine the number of moles of copper required to hold a Coulomb of charge. Note the answer is not one.

Is that what you were talking about?

I think that the disjucnction to which RM was referring, was that that number should be 100 000, or 10[sup]5[/sup]

Chronos

Yep. He gave two different values for Avogadro’s number in that post. I would have let the first one slide as a typo maybe, but he used it to compute that other number.

Ahh, I see. Took me a while on that one–you may have wanted to snip a little earlier, it looked like you were referring to his reference of the Coulumb. Sure had me confused anyway–sitting here going “6.022E23 sure as heck is Avagadro’s number, and he didn’t present the first one as it.”
Then I saw, and sure felt like an idiot :slight_smile:

As much as I have always like the image of a pipeline filled with marbles of the same diameter (whenever you push one in, another pops out at the other end), it is only an analogy for charge or electro-potential displacement. The pendulum toy is more a accurate descriptor for AC effects, but (work with me here, crowd), as has been said when DC is at work very strange things happen. When the current flow exceeds the Ampacity (new buzz word for, current carrying capacity) of a conductor, you get (tah-dah) electromigration. This involves actual atoms of the conductor’s material (usually gold or aluminum in the case of silicon microcircuit bonding wires) being “knocked” downstream by the DC flow of current. Yes Virginia, with DC things are really flowing down a pipeline, much like reality. When it comes to AC, it’s a whole different ball game. Much like the old reciprocating treadles of an ancient lathe or drill, so too, does AC power deliver its electromotive effect. Mr. Physics will intervene here if I am or am not mistaken (this is know as hedging your bet).