$A$ conducting rod of length $\ell$ moves with a velocity $V$ in a uniform magnetic field $B$ perpendicular to the plane of the rails. $A$ capacitor of capacitance $C$ is connected across the rails as shown. Find the charge on the capacitor due to the induced emf in the rod.

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec{B}$ exists parallel to the axis of rotation. The $e.m.f.$ induced between two ends of the rod is

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:

$A$ rectangular loop has a sliding connector $PQ$ of length $2\ m$ and resistance $10\Omega$. It is moving with a speed $5\ m/s$ as shown. The set-up is placed in a uniform magnetic field $3\ T$ directed into the plane of the paper. Find the three currents $I_1$,$I_2$,and $I$.

$A$ rod of length $l$ rotates with a uniform angular velocity $\omega$ about an axis passing through its middle point but normal to its length in a uniform magnetic field of induction $B$ with its direction parallel to the axis of rotation. The induced $emf$ between the two ends of the rod is