$A$ metallic rod of length $20 \,cm$ is placed in the North-South direction and is moved at a constant speed of $20 \,m/s$ towards the East. The horizontal component of the Earth's magnetic field at that place is $4 \times 10^{-3} \,T$ and the angle of dip is $45^{\circ}$. The emf induced in the rod is ............. $mV$.

$A$ rectangular loop with a sliding connector of length $l = 1.0 \, m$ is situated in a uniform magnetic field $B = 2 \, T$ perpendicular to the plane of the loop. The resistance of the connector is $r = 2 \, \Omega$. Two resistors of $6 \, \Omega$ and $3 \, \Omega$ are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity $v = 2 \, m/s$ is ........ $N$.

$A$ metal disc rotates freely between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the center (axle) and the edge of the disc,respectively. What current,if any,flows through $R$?

$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

The loop shown moves with a velocity $v$ in a uniform magnetic field of magnitude $B$,directed into the paper. The potential difference between $P$ and $Q$ is $e$. Then:

$A$ rod of length $l$,mass $m$,and resistance $R$ slides without friction down parallel conducting rails as shown in the figure. The rails are connected together at the bottom. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform vertical magnetic field $B$ exists throughout the region. Then the induced $emf$ in the loop,at the time the rod slides down with a speed $v$,is