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

$A$ fighter plane of length $20\, m$, wing span (distance from tip of one wing to the tip of the other wing) of $15\,m$ and height $5\,m$ is flying towards east over Delhi. Its speed is $240\, ms^{-1}$. The earth's magnetic field over Delhi is $5 \times 10^{-5}\,T$ with the declination angle $\, 0^\circ$ and dip of $\theta$ such that $\sin \theta = 2/3$. If the voltage developed is $V_B$ between the lower and upper side of the plane and $V_W$ between the tips of the wings, then $V_B$ and $V_W$ are close to:

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 2\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\,\mu F$ is connected as shown in the figure. Then

Two $U$-shaped tubes are moving inside each other as shown in the figure. If the length of each tube is $l$ and they move with velocity $v$ in a magnetic field $B$,what is the induced $emf$ in the circuit?

Consider the situation shown in the figure. The wire $PQ$ has a negligible resistance and is made to slide on the three rails with a constant speed of $5 \, cm/s$. Find the current in the $10 \, \Omega$ resistor when the switch $S$ is connected to the middle rail. (Given: $B = 1.0 \, T$) (in $mA$)

$A$ boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} \text{ T}$ and is directed due north and horizontal. The boat carries a vertical aerial $2 \text{ m}$ long. If the speed of the boat is $1.5 \text{ m/s}$,calculate the magnitude of the induced $emf$ in the aerial wire in $mV$.