$A$ metallic conductor of length $1 \; m$ rotates in a vertical plane parallel to the east-west direction about one of its ends with an angular velocity of $5 \; rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4} \; T$,then the emf induced between the two ends of the conductor is .............

$A$ wire loop is rotated in a magnetic field. The frequency of change of direction of the induced $e.m.f.$ is

Two rails of a railway track,insulated from each other and the ground,are connected to a millivoltmeter. What is the reading of the voltmeter when a train travels with a speed of $180 \ km/hr$ along the track? Given that the vertical component of the Earth's magnetic field is $0.2 \times 10^{-4} \ Wb/m^2$ and the rails are separated by $1 \ m$.

$XPQY$ is a vertical smooth long loop having a total resistance $R$,where $PX$ is parallel to $QY$ and the separation between them is $l$. $A$ constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. $A$ rod $CD$ of length $L$ $(L > l)$ and mass $m$ is made to slide down from rest under gravity as shown in the figure. The terminal speed acquired by the rod is . . . . . . $m/s$. ($g$ = acceleration due to gravity)

$A$ metal conductor of length $1 \ m$ rotates vertically about one of its ends at an angular velocity of $5 \ rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4} \ T$,then the e.m.f. developed between the two ends of the conductor is:

$A$ coil of $N$ turns and mean cross-sectional area $A$ is rotating with uniform angular velocity $\omega$ about an axis at right angle to a uniform magnetic field $B$. The induced e.m.f. $E$ in the coil will be