A person pedals a stationary bicycle. The pedals of the bicycle are attached to a \( 200 \) turn coil of area \( 100\ \mathrm{cm^{2}} \). The coil rotates such that it completes one revolution in \( 2\ \mathrm{s} \) and it is placed in a uniform magnetic field of \( 10\ \mathrm{mT} \) perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 62.8\ \mathrm{mV} \)
A coil rotating in a uniform magnetic field is an ac generator. Its flux is \( \Phi = NBA\cos\omega t \), so the peak emf is \( \varepsilon_{0} = NBA\omega \).
\( N = 200,\ A = 100\,\mathrm{cm^{2}} = 100\times10^{-4}\,\mathrm{m^{2}} = 10^{-2}\,\mathrm{m^{2}} \)
\( B = 10\,\mathrm{mT} = 10^{-2}\,\mathrm{T},\ T = 2\,\mathrm{s} \)
\( \displaystyle \omega = \frac{2\pi}{T} = \frac{2\pi}{2\,\mathrm{s}} = \pi\,\mathrm{rad\,s^{-1}} \)
\( \varepsilon_{0} = NBA\omega = (200)(10^{-2}\,\mathrm{T})(10^{-2}\,\mathrm{m^{2}})(\pi\,\mathrm{rad\,s^{-1}}) \)
\( \varepsilon_{0} = 2\pi\times10^{-2}\,\mathrm{V} = 62.8\,\mathrm{mV} \)
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 – …
