A bar magnet is passing through a conducting loop of radius R with velocity υ. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve :

Solution

Physics sir · 5 steps

Flux rises as the magnet enters and falls as it leaves, so the two emf pulses must have opposite signs.

1. Magnet entering. As the N end comes up to the loop and passes through it, the field lines through the loop grow quickly. So the flux Φ is increasing, and e = -dΦ/dt gives a sharp negative pulse.
2. Magnet inside. While the long middle of the magnet is passing through, the flux through the loop stays almost constant. So dΦ/dt ≈ 0 and the emf is nearly zero.
3. Magnet leaving. As the S end passes through and moves away, the flux decreases back to zero. Now -dΦ/dt is positive, so the second pulse is positive.
4. Gap between pulses. The two pulses come when the two ends of the magnet cross the loop. The ends are a distance l apart and move at speed v, so the pulses are l/v apart in time.
5. So. The curve is a negative pulse, then a flat gap of l/v, then a positive pulse. That is option (c).

The idea to keep. When a magnet passes through a loop, flux first rises and then falls. Rising and falling flux give emfs of opposite sign, and with e = -dΦ/dt the rising part gives the negative pulse.

Answer from the NTA final answer key. Solution by PrepWiser.