Assertion: $A$ current continues to flow in a superconducting coil even after the switch is off.
Reason: Superconducting coils show the Meissner effect.

The magnetic field in the region shown in the figure increases at a constant rate of $20 \, mT/sec$. Each side of the square loop $ABCD$ has a length of $1 \, cm$ and a resistance of $4 \, \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed.

Plane figures made of thin wires of resistance $R = 50 \text{ m}\Omega/\text{m}$ are located in a uniform magnetic field perpendicular to the plane of the figures, which decreases at the rate $dB/dt = 0.1 \text{ mT/s}$. Find the currents in the inner and outer boundary. (The inner radius $a = 10 \text{ cm}$ and outer radius $b = 20 \text{ cm}$)

Two different coils have inductances $L_1 = 4 \ mH$ and $L_2 = 2 \ mH$. At a certain instant,the current in the two coils is increasing at the same constant rate,and the power supplied to the first coil is four times that of the second coil. If $e$,$I$,and $U$ indicate the potential difference,current,and energy stored in the inductance respectively,then which of the following is correct?

$A$ source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t=0$,the switch is closed and current begins to flow. Which of the following options is/are correct?
$[A]$ After a long time,the current through $L_1$ will be $\frac{V}{R} \frac{L_2}{L_1+L_2}$
$[B]$ After a long time,the current through $L_2$ will be $\frac{V}{R} \frac{L_1}{L_1+L_2}$
$[C]$ The ratio of the currents through $L_1$ and $L_2$ is fixed at all times $(t>0)$
$[D]$ At $t=0$,the current through the resistance $R$ is $\frac{V}{R}$

$A$ solenoid is oriented end-on so that its opening is perpendicular to the circuit containing the two light bulbs as drawn in figure $C_1.$ For figures $C_2$ and $C_3,$ a shorting wire of negligible resistance is added as shown. Assume that the magnetic field from the solenoid,shown coming out of the plane of the page,decreases uniformly with time at the same rate for each circuit. Rank the circuits for the brightness of the bulb labeled $R_1$ from brightest to dimmest.