$A$ 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 $e.m.f.$ when it has rotated through $90^{\circ}$ is

$A$ boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \text{ T}$ due north and horizontal. The boat carries a vertical conducting rod $2 \text{ m}$ long. If the speed of the boat is $2.00 \text{ m/s}$, the magnitude of the induced e.m.f. in the rod is: (in $\text{ mV}$)

The figure shows an apparatus suggested by Faraday to generate electric current from a flowing river. Two identical conducting plates of length $a$ and width $b$ are placed parallel facing one another on opposite sides of the river flowing with velocity $u$ at a distance $d$ apart. Now both the plates are connected by a load resistance $R$. Then the current through the load $R$ is: (Consider the vertical component of the magnetic field produced by the earth is $B_v$ and the resistivity of river water is $\rho$.)

$A$ conducting rod $AB$ moves parallel to the $X-$ axis in a uniform magnetic field,which is directed perpendicular to the plane of motion (outwards). The end $A$ of the rod gets:

$A$ wheel of radius $2 \, m$ having $8$ conducting concentric spokes is rotating about its geometrical axis with an angular velocity of $10 \, rad \, s^{-1}$ in a uniform magnetic field of $0.2 \, T$ perpendicular to its plane. The value of induced emf between the rim of the wheel and the centre is . . . . . . $V$.

$A$ horizontal telegraph wire of length $30 \ m$ spread east to west falls freely from a height of $20 \ m$. If the resistance of the wire is $40 \ \Omega$ and the horizontal component of the earth's magnetic field at the place is $2 \times 10^{-5} \ T$,then the induced current when the wire reaches the ground is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)