In how many of the following cases is a current induced in the closed loop?
(a) The loop moves without rotating and stays wholly inside a uniform magnetic field.
(b) The loop is held at rest between the poles of a very strong magnet.
(c) The loop is turned in a uniform magnetic field so that the angle between the field and its plane changes.
(d) The loop lies normal to a uniform magnetic field and is stretched so that its area increases.
(e) The loop and a bar magnet move together with the same velocity.
(f) The loop moves normal to the uniform electric field between the plates of a large charged capacitor.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Two
A current is induced in a closed loop only when the magnetic flux through it changes with time. The flux \( BA\cos\theta \) changes when \( B \), \( A \) or \( \theta \) changes.
The cases in which a current is induced:
(c) Turning the loop — the angle changes
(d) Stretching the loop — the area changes
The cases in which no current is induced:
(a) The loop stays wholly inside the uniform field, so the flux through it does not change.
(b) The loop and the magnet are both at rest. The flux is large but it stays constant.
(e) The loop does not move with respect to the magnet, so the flux stays the same.
(f) An electric field cannot induce a current in the loop. Only a change of magnetic flux can.
Number of cases with an induced current = 2
NCERT (2026-27):
Faraday’s Law of Induction – “… The flux can also be altered by changing the shape of a coil (that is, by shrinking it or stretching it) in a magnetic field, or rotating a coil in a magnetic field such that the angle θ between B and A changes. In these cases too, an emf is induced in the respective coils.”
Example 6.4 – “Note that there are no induced current as long as the loops are completely inside or outside the region of the magnetic field.”
Example 6.5 – “(a) No. However strong the magnet may be, current can be induced only by changing the magnetic flux through the loop.”
Example 6.5 – “(b) No current is induced in either case. Current can not be induced by changing the electric flux.”