$A$ 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......$V$.

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 $1 \ m$.

Find out $V_A - V_B = ?$

$A$ copper rod of length $l$ is rotated about one end perpendicular to the magnetic field $B$ with constant angular velocity $\omega$. The induced e.m.f. between the two ends is

$A$ metallic square loop $ABCD$ is moving in its own plane with velocity $v$ in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced:

$XPQY$ 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)