• # question_answer A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B with an angular velocity $\omega$about an axis perpendicular to the field. If initially the plane of the coil is perpendicular to the field, then the average induced $emf$ when it has rotated through $90{}^\circ$. is A)  $\frac{\omega BA}{\pi }$              B)  $\frac{\omega BA}{2\pi }$ C) $\frac{\omega BA}{4\pi }$                D)  $\frac{2\omega BA}{\pi }$

$\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{15a}{3a}=\frac{5}{1}$ Flux passing through the area of the coil when it is far to magnetic field $\Rightarrow$ and ${{T}_{1}}:{{T}_{2}}=5:1$ Flux passing through the area of the coil when it is $T=M\,\left( g-\frac{g}{4} \right)=\frac{3Mg}{4}$ to the magnetic field $W=\mathbf{T}\cdot \mathbf{d}\Rightarrow \,W=Td$ $\Rightarrow$ $W=-Td=-\frac{3Mgd}{4}$ But       $\Sigma mvr=\,({{l}_{system}})\omega$ $\Rightarrow$            $mv\frac{l}{2}=\frac{(2m)\,{{(2l)}^{2}}}{12}\omega =\frac{2m(4{{l}^{2}})}{12}\omega$