Answer:
From Faraday's law of Induction: A changing magnetic field induces emf in the coil.
Step-by-step explanation:
Faraday's law states that when a coil is run through a changing magnetic field or a magnet is passed back and forth through a coil, an emf is induced which produces electric current in the coil.
Changing magnetic flux induces electromotive force.

When the magnet is passed back and forth, it causes a changing magnetic flux around the coil. This induces emf and the current flows which lights up the bulb connected to it.