#### A circular coil of radius 10 cm is placed in a uniform magnetic field of with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2s. The maximum value of EMF induced in the coil will be close to the integer_________ Option: 1 15 Option: 2 10 Option: 3 3 Option: 4 63

Given

$\\\begin{array}{l} r=0.1 \mathrm{~m} \\ and \ \quad \frac{\mathrm{T}}{2}=0.2 \mathrm{sec} \Rightarrow \quad \mathrm{~T}=0.4 \ \mathrm{sec} \\ \mathrm{B}=3 \times 10^{-5} \mathrm{T} \end{array}$

\begin{aligned} &\text { At any time }\\ &\text { flux } =\phi=B A \cos \omega t\\ &|\mathrm{emf}|=\left|\frac{\mathrm{d} \phi}{\mathrm{dt}}\right|=|\mathrm{BA} \omega \sin \omega \mathrm{t}|\\ &(\mathrm{emf})_{\max }=\mathrm{BA} \omega=\mathrm{BA} \frac{2 \pi}{\mathrm{T}}\\ &=\frac{3 \times 10^{-5} \times \pi \times(0.1)^{2} \times 2 \pi}{0.4}\\ &=\frac{6 \pi^{2}}{4} \times 10^{-6} &\left(\begin{array}{c} Use \ \pi^{2} \simeq 10 \end{array}\right)\\ &=15 \times 10^{-6}\\ &=15 \mu \mathrm{V} \end{aligned}