Two parallel rails of a railway track, insulated from each other and from the ground, are connected to a millivoltmeter. The distance between the rails is $1 \, m$. $A$ train is travelling with a velocity of $72 \, km/h$ along the track. What is the reading of the millivoltmeter (in $mV$)? (The vertical component of the Earth's magnetic induction is $2 \times 10^{-5} \, T$.)

Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time $t=0$,its left arm passes the origin,$O$. If for $t \geq 0$,the current in the loop is $I$ and the distance of its left arm from the origin is $x$,then $I$ versus $x$ graph will be

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the magnitude of potential differences.

$A$ vertical rod of length $l$ is moved with constant velocity $v$ towards the east. If the vertical component of the Earth's magnetic field is $B$ and the angle of dip is $\theta$,then the induced $emf$ in the rod is:

$A$ conducting circular loop is placed in a uniform magnetic field of $0.04\, T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of $2\, mm/s$. The induced $emf$ in the loop when the radius is $2\, cm$ is:

$A$ 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