$A$ very long solenoid of radius $R$ is carrying current $I(t) = kt e^{-\alpha t}$ $(k > 0)$,as a function of time $(t \geq 0)$. Counter-clockwise current is taken to be positive. $A$ circular conducting coil of radius $2R$ is placed in the equatorial plane of the solenoid and is concentric with the solenoid. The induced current in the outer coil as a function of time is correctly depicted by:

If an iron rod is placed inside a coil, what happens to the induced current?

$A$ coil having $N$ turns and resistance $R$ $\Omega$ is connected to a galvanometer of resistance $6R$ $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time $t$ second. The induced current in the circuit is

In the $LR$ circuit shown,what is the variation of the current $I$ as a function of time? The switch is closed at time $t = 0 \, s.$

$A$ small bar magnet is moved through a coil at a constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer $G$ attached across the coil? Three positions shown describe: $(a)$ the magnet's entry,$(b)$ the magnet is completely inside,and $(c)$ the magnet's exit.

$A$ metallic ring of mass $m$ and radius $l$ (ring being horizontal) is falling under gravity in a region having a magnetic field. If $z$ is the vertical direction,the $z$-component of the magnetic field is $B_z = B_0(1 + \lambda z)$. If $R$ is the resistance of the ring and the ring falls with a velocity $v$,find the energy lost in the resistance per unit time. If the ring has reached a constant velocity,use the conservation of energy to determine $v$ in terms of $m, B_0, l, \lambda, R$ and acceleration due to gravity $g$.