A girl pedals a stationary bicycle. The pedals of the bicycle are attached to a 100 turn coil of area \( 0.10\,\mathrm{m^2} \). The coil completes one revolution in two seconds, and it is placed in a uniform magnetic field of 0.02 T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.628 V
A coil rotating in a uniform magnetic field works as an ac generator. Its flux changes as \( NBA\cos\omega t \), so the induced emf is \( NBA\omega\sin\omega t \) and its peak value is
\( \displaystyle e_0 = N B A \omega \)
The coil makes one revolution in 2 s, so its angular speed is
\( \displaystyle \omega = \frac{2\pi}{T} = \frac{2\pi}{2\,\mathrm{s}} = \pi\,\mathrm{rad\,s^{-1}} \)
\( N = 100 \)
\( B = 0.02\,\mathrm{T} \)
\( A = 0.10\,\mathrm{m^2} \)
\( \displaystyle e_0 = 100 \times 0.02 \times 0.10 \times \pi = 0.2\pi\,\mathrm{V} = 0.628\,\mathrm{V} \)
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
AC Generator – …
