It did not work that way, and today, knowing about energy, we can guess why: an electric current in a wire needs a constant supply of energy, and where would that come from?
However, Faraday found a somewhat similar result, if the magnetic field in the coil was undergoing change, as happens (for instance) as the bar magnet is being pushed into the coil, or being pulled out. During those changes, a momentary current did flow. Faraday called this electromagnetic induction, creating an “induced current.” See for instance http://www.phy6.org/earthmag/dynamos.
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