When a magnet is moved into and out of the solenoid, magnetic flux is being cut by the coil.
The cutting of magnetic flux by the wire coil induces an e.m.f in the wire.
When the solenoid is connected to a closed circuit, the induced current will flow through the circuit.
The production of electric current by changing magnetic field is called electromagnetic induction.
Current/emf is induced only when there is relative motion between the magnetic field and the conductor.
The direction of the induced current and the magnitude of the induced e.m.f due to the cutting of the magnetic flux can be determined from Lenz's Law and Faraday's Law.
Lenz's Law
When a magnet is moved into and out of a coil, the induced current that flows through the coil can be determined from Lenz's Law.
Lenz's Law states that the induced current always flows in the direction that opposes the change in magnetic flux.
Lenz's Law obeys the principle of conservation of energy. Work is done to move the magnet against the repulsive force. This work done is converted to electric energy which manifests as an induced current.
For a conductor in a closed circuit moving perpendicular to a magnetic field and hence cutting its magnetic flux, the direction of the induced current is determined from Fleming's Right-Hand Rule.
Fleming's Right-Hand Rule is used to determine the direction of the induced current that flows from the wire when there is relative motion with respect to the magnetic field
