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# A circular coil of radius $30\; cm$ and resistance $\pi^{2}\;Ohms$ is rotating in a uniform magnetic field $B=10^{-2}$. Axis of rotation is diameter of coil which is perpendicular to direction of B. If Coil rotates with $200\;rpm$ the current induced in coil is

$(a)\;30\;mA \\ (b)\;6 \pi^2 mA \\(c)\;6 \;mA \\(d)\;30 \pi ^2 mA$

The induced emf $e_o$
$e_o=WNBA$
where $w=2 \pi v$
$\qquad= 2 \times \pi \large\frac{200}{60}$
$R=\pi^2$ ohms,radius $r=0.3\;m$
$i_0=\large\frac{e_o}{R}$
$\qquad= \large\frac{2 \pi \times \Large\frac{200}{60} \times \large 1 \times 10^{-2} \pi (0.3)^2}{\pi^2}$
$\qquad= 6 \times 10^{-3}$
$\qquad= 6\;mA$
Hence c is the correct answer.