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Not very far. Assuming the speed of light, which is a liberal assumption, an electron would only travel 16.7 ms (1/60 Hz) times 3 x 108 m/s (c) or about 5 million meters in one cycle.
AnswerAlthough electrons move haphazardly at very great speed, when under the influence of an electric field, their actual drift along a conductor is very, very, slow. The actual drift depends upon a number of factors, but the distance involved during the period of one cycle or, more meaningfully, during one half-cycle (because the drift direction will reverse!), is likely to be only a fraction of a millimetre.
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