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(D) Let $	heta$ be the angle between the magnetic field vector $\vec{B}$ and the area vector $\vec{A}$ (which is perpendicular to the plane of the co

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Parallel to the magnetic field

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(D) Let $	heta$ be the angle between the magnetic field vector $\vec{B}$ and the area vector $\vec{A}$ (which is perpendicular to the plane of the coil).The magnetic flux through the coil is given by $\phi = \vec{B} \cdot \vec{A} = BA \cos 	heta$.Since the coil rotates with constant angular velocity $\omega$,we have $	heta = \omega t$.According to Faraday's law of induction,the induced $emf$ $(\varepsilon)$ is given by $\varepsilon = -\frac{d\phi}{dt}$.$\varepsilon = -\frac{d}{dt}(BA \cos(\omega t)) = BA\omega \sin(\omega t)$.The induced $emf$ is maximum when $\sin(\omega t) = 1$,which occurs when $\omega t = 90^{\circ}$.When $\omega t = 90^{\circ}$,the angle between the area vector and the magnetic field is $90^{\circ}$,which means the plane of the coil is parallel to the magnetic field.

$A$ rectangular coil $ABCD$ is rotated in a uniform magnetic field with constant angular velocity $\omega$ about one of its diameters as shown in the figure. The induced $emf$ will be maximum when the plane of the coil is

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