How far does the electron move?
 

Some folks *cough*Cheesehead,Xilman,etc.*cough* should sit on their hands for a while on this.

So, the big coal fired/hydro/nuke/solar power plant outside of town generates your power. It sends electricity coursing down the wires, through the electrical substation, and transformers; and on to your house. When you flip the switch and start your crunching farm (you had turned it off for it's bimonthly dusting), the wheel in the metere spins like a dervish or Tasmanian Devil. You decide to take a to reward yourself with a cup of oolong after the ordeal. So you pull out your brand new electric tea kettle (with optional knit cozy). You decrate it and rinse it with a triple wash of distilled water.
Just at the very instant (down to the femtosecond) before you plug it on the break-in boil (filled with Evian, because of it's very low TDS), Gerbil2 sneaks into your wires and snatches hold of a single electron. Acting with a speed that would make Neo look like he is stopped dead in his tracks, Gerbil2 pulls out a "magic marker" and inscribes George's initials, the date, and time on the surface of the electron. Gerbil2 then releases said electron back into the wires of your abode. The electron is placed where the wire (within the wall) passes up through the plane of the floor. You plug in the kettle (the AC power starts to flow into the kettle) and walk into the adjoining room (so that the water can boil).
You remember that you forgot your iPad on the cook top. Exactly 20 seconds after plugging in the kettle, you are again in the kitchen with iPad in hand and look for the electron. If you could spot the electron with the tiny writing, how far would it have traveled (or where would it be)?

Here are some particulars that may be asked for:
Plane of floor to centere of outlet: 1.33333333333333m
Length of cord on kettle (from tip of plug to interface with heating element): 1.5m
Total length of heating element: 24.669cm
Kettle initial contains 1L of 4ppm TDS water (assume the TDS is NaHCO[SUB]3[/SUB]) at 293.15 Kelvins, with 1L of headspace.
The wires in the wall and outlet are pure Aluminum.
The conductor of the cord and plug is pure Copper.
The heating element is composed of [URL="http://www.azom.com/Details.asp?ArticleID=863"]316 stainless steel[/URL], with a 1nm coating of HDPE.
Elevation of the kettle is 106.5m above MSL.
Everything is at 20C and 1 atm.
The AC power being supplied is 55Hz and 165V on a 150 Amp service, with a 20 Amp breaker on the line in question.

[SPOILER]Not more than a few inches - more likely under a millimeter - in either direction along the wire. After all, it's AC. Just my two cents...[/SPOILER]

[SPOILER]Have you looked down the back of the sofa?[/SPOILER]

[QUOTE=Uncwilly;250710]Everything is at 20C ...[/QUOTE]Except for the water in the kettle after 20 seconds.

[spoiler]I usually lose stuff in the wash after leaving it in my pockets, maybe your electron is there.[/spoiler]

[QUOTE=retina;250744]Except for the water in the kettle after 20 seconds.[/QUOTE]I was obviously stating initial conditions.

[QUOTE=Uncwilly;250745]I was obviously stating initial conditions.[/QUOTE]And indulging in product placement. I think we should ask how much you are being paid for all those advertisments. Wouldn't want any undeclared conflicts of interest ...

Paul

Assuming I am not one of the banned posters in the list of "Cheesehead,Xilman,etc." then [spoiler]the position of the electron will likely be just where Gerbil2 last placed it. Since "exactly 20 seconds" divides evenly into 55Hz. But as for how far the electron has moved, well that is a little bit different. Electrons sure don't move quickly but they do move a small amount, so if the electron had an odometer it would not show zero. However, right now, I don't want to resort to Google to search for the electron mobility in Aluminium, so perhaps someone else would like to compute the total distance travelled?[/spoiler]

[QUOTE=xilman;250767]And indulging in product placement. I think we should ask how much you are being paid for all those advertisments. Wouldn't want any undeclared conflicts of interest ...[/QUOTE]
Those all could be changed to generic if you want to. The link is only out to a list of properties of 316.

It seems to me that the electron would go for a random walk, but I don't know what the appropriate approximation for the number of steps or step size would be.

While - prompted by this thread - doing a bit of historical reading on AC power, I came across the fascinating history of the [url=http://en.wikipedia.org/wiki/War_of_Currents]War of the Currents[/url] between Thomas Edison (who had staked his business on DC power) and George Westinghouse (who recognied the huge advantage of AC and developed it with the help of former Edison employee Nikola Tesla. First a math-related part of the history:
[quote]From his work with rotary magnetic fields, Tesla devised a system for generation, transmission, and use of AC power. He partnered with George Westinghouse to commercialize this system. Westinghouse had previously bought the rights to Tesla`s polyphase system patents and other patents for AC transformers from Lucien Gaulard and John Dixon Gibbs.

Several undercurrents lay beneath this rivalry. Edison was a brute-force experimenter, but was no mathematician. AC cannot be properly understood or exploited without a substantial understanding of mathematics and mathematical physics (see AC power), which Tesla possessed. Tesla had worked for Edison but was undervalued (for example, when Edison first learned of Tesla`s idea of alternating-current power transmission, he dismissed it: "[Tesla`s] ideas are splendid, but they are utterly impractical."[3]). Bad feelings were exacerbated because Tesla had been cheated by Edison of promised compensation for his work.[4][5] Edison later came to regret that he had not listened to Tesla and used alternating current.[6][/quote]
[i]My Comment:[/i] I bet Edison came to regret it ... but based on the sheer viciousness of Edison`s campaign to discredit AC, more likely this was a financial regret rather than one involving any humane feelings.

And next the vicious FUD campaign waged by Edison in an effort to discredit AC and Westinghouse - this encompasses the invention of the electric chair as a marketing-smear-campaign gimmick:
[quote]Edison carried out a campaign to discourage the use[12] of alternating current, including spreading disinformation on fatal AC accidents, publicly killing animals, and lobbying against the use of AC in state legislatures. Edison directed his technicians, primarily Arthur Kennelly and Harold P. Brown,[13] to preside over several AC-driven killings of animals, primarily stray cats and dogs but also unwanted cattle and horses. Acting on these directives, they were to demonstrate to the press that alternating current was more dangerous than Edison`s system of direct current.[14] He also tried to popularize the term for being electrocuted as being "Westinghoused". Years after DC had lost the "war of the currents," in 1902, his film crew made a movie of the electrocution with high voltage AC, supervised by Edison employees, of Topsy, a Coney Island circus elephant which had recently killed three men.[15]
[b]
Edison opposed capital punishment, but his desire to disparage the system of alternating current led to the invention of the electric chair. Harold P. Brown, who was being secretly paid by Edison, built the first electric chair for the state of New York to promote the idea that alternating current was deadlier than DC.[16]
[/b]
When the chair was first used, on August 6, 1890, the technicians on hand misjudged the voltage needed to kill the condemned prisoner, William Kemmler. The first jolt of electricity was not enough to kill Kemmler, and only left him badly injured. The procedure had to be repeated and a reporter on hand described it as "an awful spectacle, far worse than hanging." George Westinghouse commented: "They would have done better using an axe." [17][/quote]

My guess: [SPOILER]Only a tiny proportion of the electrons present in the wire need to jump to new molecules all together in the appropriate direction to produce current sufficient for the kettle to operate. The most likely distance traveled by the marked electron is zero, give or take the normal quantum effects. Next most likely is the distance to the next molecule (itself a highly variable distance). In general the current is produced by mass motion of a small proportion of all the electrons, and each individual electron will only move a short distance before others take over the mass movement.
[/SPOILER]