You can flip a light switch and watch a lamp five feet away turn on in an instant. But to watch a single electron travel from the switch to the light, you'd have to wait over an hour. The speed at which electrons move through a wire is called "electron drift," and it happens at around 0.1-0.4 millimeters per second. Pit an electron against your average snail, which travels around 3-10 millimeters per second, and it's not even a contest. But if electrons move so slowly, how can a switch turn on a lamp instantaneously? Think of a tube filled with marbles: if you add a marble at one end, a marble will come out the other end at almost the same instant, even though each marble didn't move that far on its own. Likewise, a copper wire contains lots of electrons (8.5x10^28 per cubic meter, to be exact). Those electrons are packed in so tightly that even a small movement will travel down the wire from electron to electron at an impressive speed, letting you turn on the lights without having to wait for electrons to travel the whole way there.
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