The magnetic flux linked with a coil rises steadily from zero to 6 mWb in the first 2 s, stays at 6 mWb for the next 4 s and then falls steadily to zero in the next 1 s. During which time interval is the magnitude of the emf induced in the coil the largest?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 s to 7 s
The magnitude of the induced emf equals the rate of change of magnetic flux. A large flux that stays steady induces no emf. A flux that changes quickly induces a large emf.
Call the emf in the intervals 0 to 2 s, 2 s to 6 s and 6 s to 7 s \( \varepsilon_1 \), \( \varepsilon_2 \) and \( \varepsilon_3 \). Then:
\( \begin{aligned} |\varepsilon_1| &= \frac{6\,\mathrm{mWb}}{2\,\mathrm{s}} \\ &= 3\,\mathrm{mV} \end{aligned} \)
\( |\varepsilon_2|=0 \)
\( \begin{aligned} |\varepsilon_3| &= \frac{6\,\mathrm{mWb}}{1\,\mathrm{s}} \\ &= 6\,\mathrm{mV} \end{aligned} \)
Option (1) 0 to 2 s — Incorrect. The flux rises by 6 mWb here, but it takes 2 s. So the emf is only 3 mV, half of that in the last interval.
Option (2) 2 s to 6 s — Incorrect. The flux has its largest value in this interval, but it does not change, so no emf is induced.
Option (3) 6 s to 7 s — Correct. The whole 6 mWb disappears in only 1 s. This is the fastest change of flux in the three intervals, so the emf of 6 mV is the largest.
Option (4) It is equal in the intervals 0 to 2 s and 6 s to 7 s — Incorrect. The change of flux is 6 mWb in both intervals, but the times are different. The emf depends on the rate of change of the flux.
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.”