A loop of flexible wire lies with its plane normal to a uniform magnetic field of 0.4 T. The loop is pulled into a narrow shape, and its area falls from 300 cm2 to 100 cm2 in 0.2 s. The average emf induced in the loop is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(40\ \mathrm{mV}\)
The field and its angle with the loop stay the same. The flux \( BA \) changes only because the area changes, so the emf is \( B\,\Delta A/\Delta t \). The area falls by \( 300-100=200\ \mathrm{cm^{2}} \).
\( B=0.4\ \mathrm{T} \)
\( \Delta A=200\ \mathrm{cm^{2}}=0.02\ \mathrm{m^{2}} \)
\( \Delta t=0.2\ \mathrm{s} \)
\( \begin{aligned} \varepsilon &= \frac{B\,\Delta A}{\Delta t} \\ &= \frac{0.4\times0.02}{0.2} \\ &= 0.04\ \mathrm{V} \\ &= 40\ \mathrm{mV} \end{aligned} \)
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.”
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.”