A coil of 200 turns, area $0.20 m^2$ 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

$7.04 \times 10^{-2} V$

The correct answer is Option (4) → $7.04 \times 10^{-2} V$

We know, $\phi=\vec{B} . \vec{A}$

$\Rightarrow \phi=B A \cos \theta$  and  $\theta=\omega t$

$\Rightarrow \phi=N B A \cos (\omega t), \varepsilon=\frac{-d \phi}{d t}$

$\Rightarrow \varepsilon=N B A \omega \sin (\omega t) \Rightarrow \varepsilon_{\max }=N B A \omega$

$\Rightarrow \varepsilon_{\max }=0.4 \times 10^{-4} \times \frac{20}{100} \times 7 \times 2 \pi \times 200$

$\Rightarrow \varepsilon_{\max }=0.8 \times \frac{14 \pi}{5} \times 10^{-2}=7.04 \times 10^{-2} V$