In which of the following cases is the emf induced in the coil larger…

The correct answer is Option (2) → It is larger in case 1

By Faraday’s law, the induced emf equals the rate of change of magnetic flux through the coil. The flux changes because of the relative motion of the magnet and the coil. The faster this motion, the faster the flux changes.

Option (1) It is the same in both cases — Incorrect. Moving the coil instead of the magnet gives the same effect only at the same speed. Here case 2 is slow, so its flux changes at a smaller rate.

Option (2) It is larger in case 1 — Correct. The magnet moved quickly changes the flux through the coil in a shorter time, so \( \Delta\Phi_B/\Delta t \) is larger. The induced emf is larger too.

Option (3) It is larger in case 2 — Incorrect. Moving the coil in place of the magnet does not by itself increase the emf. Also, the slow motion gives a smaller rate of change of flux.

Option (4) It cannot be predicted — Incorrect. Faraday’s law relates the emf to the rate of change of flux, so the faster relative motion predicts the larger emf.

NCERT (2026-27):
The Experiments of Faraday and Henry – “… Further, the deflection (and hence current) is found to be larger when the magnet is pushed towards or pulled away from the coil faster. Instead, when the bar magnet is held fixed and the coil C₁ is moved towards or away from the magnet, the same effects are observed.”

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.”