A circular coil of area \( 300\,\mathrm{cm^2} \) and 25 turns rotates about its vertical diameter with an angular speed of \( 40\,\mathrm{rad\,s^{-1}} \) in a uniform horizontal magnetic field of magnitude 0.05 T. The maximum voltage induced in the coil is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.5 V
For a coil rotating in a uniform field, the flux is \( \Phi = NBA\cos\omega t \), and Faraday's law gives \( \varepsilon = NBA\omega\sin\omega t \). The maximum emf is the amplitude.
\( \displaystyle \varepsilon_0 = N B A \omega \)
\( N = 25 \)
\( B = 0.05\,\mathrm{T} \)
\( A = 300\,\mathrm{cm^2} = 3\times10^{-2}\,\mathrm{m^2} \)
\( \omega = 40\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle \varepsilon_0 = 25 \times 0.05 \times 3\times10^{-2} \times 40 = 1.5\,\mathrm{V} \)