$A$ train is moving with a speed of $30 \, m \, s^{-1}$ in the north-south direction on rails separated by $2 \, m$. If the vertical component of the Earth's magnetic field is $8 \times 10^{-5} \, T$,the induced $e.m.f.$ is: (in $, V$)

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

$A$ horizontal wire is free to slide on the vertical rails of a conducting frame as shown in the figure. The wire has a mass $m$ and length $l$,and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame,find the terminal speed of the wire as it falls under the force of gravity.

The magnetic field in a region is given by $\vec B = B_0(1 + \frac{x}{a})\hat k$. $A$ square loop of edge length $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec V = V_0\hat i$. The $emf$ induced in the loop is:

$A$ uniform magnetic field exists in the region given by $\vec{B} = 3\hat{i} + 4\hat{j} + 5\hat{k} \, T$. $A$ rod of length $L = 5 \, m$ placed along the $y$-axis is moved along the $x$-axis with a constant speed $v = 1 \, ms^{-1}$. The induced e.m.f. in the rod 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 $1 \ m$.