The variation of induced emf $(E)$ with time $(t)$ in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as

$A$ 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.

$A$ coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time $t = 0$,so that a time-dependent current $I_1(t)$ starts flowing through the coil. If $I_2(t)$ is the current induced in the ring and $B(t)$ is the magnetic field at the axis of the coil due to $I_1(t)$,then as a function of time $(t > 0)$,the product $I_2(t) B(t)$:

As per the given figure,if $\frac{ dI }{ dt } = -1 \text{ A/s}$,then the value of $V_{AB}$ at this instant will be $.......... \text{ V}$.

The current $I$ through a coil varies with time $t$ as shown in the graph. Plot the graph for the induced $emf$ $e$ versus time $t$ for the coil.

The switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced emf in the inductor $L$ and $i$ denotes the current flowing through the circuit at time $t$,which of the following graphs correctly represents the variation of $e$ with time $t$?