A rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the x-axis with a constant velocity $v_0$ in the plane of the paper. At $t=0$, the right edge of the loop enters a region of length $3L$ where there is a uniform magnetic field $B_0$ into the plane of the paper, as shown in the figure. For sufficiently large $v_0,$ the loop eventually crosses the region. Let $x$ be the location of the right edge of the loop. Let $v\left(x\right)$, $I\left(x\right)$ and $F\left(x\right)$ represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of $x$. Counter-clockwise current is taken as positive.



Which of the following schematic plot(s) is(are) correct ? (Ignore gravity)

In the circuit shown below, the key is pressed at time $t=0$. Which of the following statement(s) is(are) true?

A long straight wire carries a current, $I=2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances $1 \mathrm{cm}$ and $4 \mathrm{cm}$ from the wire.  At time $t=0$, the rod starts moving on the rails with a speed $v=3.0 \mathrm{m} {\mathrm{s}}^{-1}$ (see the figure).

A resistor $R=1.4 \mathrm{\Omega }$ and a capacitor $C_0=5.0 \mathrm{\mu F}$ are connected in series between the rails. At time $t=0$, $C_0$ is uncharged. Which of the following statement(s) is (are) correct? [${\mu }_0=4\pi \times {10}^{-7}$ SI units. Take $\ln 2=0.7$]

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)