$A$ train with an axle of length $1.66 \ m$ is moving towards north with a speed of $90 \ km/h$. If the vertical component of the earth's magnetic field is $0.2 \times 10^{-4} \ T$,the emf induced across the ends of the axle of the train is: (in $mV$)

$A$ rectangular loop of length $l$ and breadth $b$ is placed at a distance of $x$ from an infinitely long wire carrying current $i$ such that the direction of the current is parallel to the breadth of the loop. If the loop moves away from the current-carrying wire in a direction perpendicular to it with a velocity $v$,the magnitude of the induced emf in the loop is: ($\mu_0=$ permeability of free space)

$A$ conducting rod of length $L = 0.1 \, m$ is moving with a uniform speed $v = 0.2 \, m/s$ on conducting rails in a magnetic field $B = 0.5 \, T$ as shown. On one side,the end of the rails is connected to a capacitor of capacitance $C = 20 \, \mu F$. Then the charges on the capacitor plates $A$ and $B$ are:

$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

$A$ conducting rod of mass $m$ and length $l$ is free to move without friction on two parallel long conducting rails,as shown in the figure. There is a resistance $R$ across the rails. In the entire space,there is a uniform magnetic field $B$ normal to the plane of the rod and rails. The rod is given an impulsive velocity $v_0$. What happens to the initial kinetic energy $\frac{1}{2} m v_0^2$?

$A$ 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: