A coil of 200 turns, area \( 0.20\,\mathrm{m^2} \) is rotated in a uniform magnetic field of 0.4 G perpendicular to the axis of the coil at the rate of 7 rps. The maximum emf induced in the coil is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 7.04 \times 10^{-2}\,\mathrm{V} \)
For a coil rotating in a uniform field, the flux is \( \Phi = NBA\cos\omega t \). By Faraday's law the induced emf is
\( \displaystyle \varepsilon = -\frac{d\Phi}{dt} = NBA\omega\sin\omega t \;\Rightarrow\; \varepsilon_{\max} = NBA\omega \)
\( B = 0.4\,\mathrm{G} = 0.4\times10^{-4}\,\mathrm{T} \)
\( \omega = 2\pi \times 7\,\mathrm{rps} = 14\pi\,\mathrm{rad\,s^{-1}} \approx 43.98\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle \varepsilon_{\max} = 200 \times 0.4\times10^{-4}\,\mathrm{T} \times 0.20\,\mathrm{m^2} \times 43.98\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle \varepsilon_{\max} = 1.6\times10^{-3} \times 43.98 \approx 7.04\times10^{-2}\,\mathrm{V} \)