the voltage flips back and forth as the magnet spins beneath the coil The magnet has two poles, and the current flows in opposite directions under the influence of each pole. a variation on the left-hand rule, in a way. Moving the poles (or the wire, same difference) puts any given place in the wire under the influence of opposite poles half the time.
The frequency of the current (its regular rate of reversal) is a function of the rate of the turning of the coil or magnet.
There is energy in the motion of the electrons without regard to which way they are moving. Normally, under one-directional processes like water flow, you would need to put energy back in to make the water flow the other direction, but this does not apply with a/c electricity because the poles are always converting mechanical energy into electricity, without regard to direction of flow. The magnet polarity is the reason. Magnets have two poles and the electrons will move in opposite directions depending on the polarity of the magnet. No requirement for putting energy back in when going the other way, as one might expect. More like a swinging clock pendulum, although not the best analogy.
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