Move a magnet rapidly through a coil and an LED may flash. It is a satisfying demonstration of induction, but it is also a good place to learn the difference between generating electricity and creating energy.
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The source is motion
Your hand does mechanical work when it moves the magnet. The changing magnetic flux induces a voltage in the coil. When current flows into a load, the magnetic interaction resists the motion. That resistance is part of energy conservation: extracting more electrical power requires more mechanical input.
How to improve the experiment
Try more turns of wire, stronger magnets, a smaller air gap and faster controlled motion. Then compare the open-circuit voltage with the voltage while powering a load. The difference reveals internal resistance and loading effects.
What a generator adds
A practical generator simply arranges continuous relative motion between magnetic fields and conductors. A turbine, engine, hand crank, wind rotor or falling water supplies the mechanical energy. The coil-and-magnet experiment is therefore not a toy version of impossible free energy. It is a miniature version of the same physics used in power stations.