$A$ 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:

$A$ thin wire of length $2\,m$ is placed perpendicular to the $x-y$ plane. It is moved with velocity $\overrightarrow v = (2\hat i + 3\hat j + \hat k)\,m/s$ through a region of magnetic induction $\overrightarrow B = (\hat i + 2\hat j)\,Wb/m^2$. The potential difference induced between the ends of the wire is......$V$.

$A$ wheel with $10$ spokes,each of length $L \ m$,is rotated with a uniform angular velocity $\omega$ in a plane normal to a magnetic field $B$. What is the emf induced between the axle and the rim of the wheel?

$A$ square metallic wire loop of side $0.1 \, m$ and resistance $1 \, \Omega$ is moved with a constant velocity in a magnetic field of $2 \, Wb/m^2$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop, and the loop is connected to a network of resistances. What should be the velocity of the loop to have a steady current of $1 \, mA$ in the loop? (in $cm/sec$)

$A$ metal disc of radius $30 \ cm$ rotates with a constant angular velocity $\omega = 100 \ rad/s$ about its axis. Find the magnitude of the potential difference between the centre and the rim of the disc if an external uniform magnetic field of induction $B = 4 \ mT$ is directed perpendicular to the disc. (in $mV$)

$A$ conducting rod $PQ$ of length $5\,m$ oriented as shown in the figure is moving with velocity $(2\,m/s)\hat{i}$ without any rotation in a uniform magnetic field $(3\hat{j} + 4\hat{k})\,T$. The $Emf$ induced in the rod is.....$V$.