$A$ 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 $mV$)

$A$ straight line conductor of length $0.4 \ m$ is moved with a speed of $7.0 \ ms^{-1}$ perpendicular to a magnetic field of intensity $0.8 \ Wb \ m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

$A$ constant magnetic field of $1 \, T$ is applied in the $x > 0$ region. $A$ metallic circular ring of radius $1 \, m$ is moving with a constant velocity of $1 \, m/s$ along the $x$-axis. At $t = 0 \, s$,the center $O$ of the ring is at $x = -1 \, m$. What will be the value of the induced $emf$ in the ring at $t = 1 \, s$? (Assume the velocity of the ring does not change.) (In $V$)

$A$ closed loop is moving with constant velocity in a uniform magnetic field as shown. The potential difference and current in element $AB$ will be:

$A$ copper rod of mass $m$ slides under gravity on two smooth parallel rails,with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom,the rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails,as shown in the figure. The terminal speed of the copper rod is

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