$A$ 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

$A$ thin semicircular conducting ring of radius $R$ is falling with its plane vertical in a horizontal magnetic induction $B$. At the position $MNQ$,the speed of the ring is $V$ and the potential difference developed across the ring is

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is:

$A$ metal disc rotates freely between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the center (axle) and the edge of the disc,respectively. What current,if any,flows through $R$?

$A$ circular disc of radius $0.1 \ m$ is rotating about its axis at a frequency of $10 \ rev/s$ in a uniform magnetic field of $0.1 \ T$ directed perpendicular to the disc. Calculate the induced $emf$ between the center and the rim of the disc.

$A$ circular conducting coil of radius $1\, m$ is being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\, \mu\Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $B = \frac{4}{\pi} \times 10^{-3} T \left(1 - \frac{t}{100}\right)$. The energy dissipated by the coil before the magnetic field is switched off completely is $E = .....\, mJ$.