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The electrical energy produce inside the coil due to changing magnetic flux on a coil . The mechanical energy of magnet or coil get converted into electrical energy(law of conservation of energy) . But , if we use solenoid instead of permanent magnet and change the magnitude of current through solenoid it induces current in the coil. so my question is , from where this electrical energy come from? It doesn't get produced by the conversion of mechanical energy.

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In effect your have a transformer which is powered by a changing current which might be produced by a generator and hence mechanical energy is a possible source.
Other sources might be sound (microphone), light (photocell), etc.

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