Question 75 of 153

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

A\(\varphi=\mathrm{AB}, \varepsilon=0\)B\(\varphi=0, \varepsilon=0\)C\(\varphi=0, \varepsilon=\mathrm{NAB} \omega\)D\(\varphi=\mathrm{AB}, \varepsilon=\mathrm{NAB} \omega\)

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Answer: (C) \(\varphi=0, \varepsilon=\mathrm{NAB} \omega\)

$\begin{aligned}
\phi & =\mathrm{BAN} \cdot \cos (\omega \mathrm{t}) \\
\varepsilon & =\frac{-\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{BA} \omega \mathrm{~N} \cdot \sin (\omega \mathrm{t})
\end{aligned}$

When $B$ is parallel to plane, $\underline{\underline{\omega t}}=\frac{\pi}{2}$
$\Rightarrow \phi=0, \varepsilon=\mathrm{BA} \omega \mathrm{~N}$