An emf is induced in a coil only when

The correct answer is Option (3) → the magnetic flux through it changes

Faraday found that an emf appears in a coil whenever the magnetic flux linked with it changes. The emf is \( \varepsilon=-\frac{d\Phi_B}{dt} \). If the flux stays constant, there is no induced emf, whatever else is present.

Option (1) a current flows through it — Incorrect. A steady current gives a constant flux, so no emf is induced. A coil with no current at all can still get an emf when a magnet is moved near it.

Option (2) the magnetic field through it changes — Incorrect. A changing field is only one way to change the flux. The flux also changes when the area of the coil changes in a steady field. So a change in the field is not needed every time.

Option (3) the magnetic flux through it changes — Correct. An emf is induced whenever the flux through the coil changes, and only then. It does not matter whether the change comes from the field, the area or the turning of the coil.

Option (4) it is connected to a battery — Incorrect. A battery only sends a current through the coil. Once this current is steady, the flux is constant and no emf is induced.

NCERT (2026-27):
Faraday’s Law of Induction – “The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.”