In an $L-R$ circuit connected to a battery,the rate at which energy is stored in the inductor is plotted against time during the growth of the current in the circuit. Which of the following best represents the resulting curve?

Two long parallel wires whose centres are at a distance $d$ apart carry equal currents in opposite directions. If the flux within the wires is neglected,the inductance of such an arrangement of wire of length $l$ and radius $a$ will be

The plane of a circular coil of resistance $7.5 \ \Omega$ is placed perpendicular to a uniform magnetic field. The flux $\phi$ (in weber) through the coil varies with time $t$ (in second) as $\phi = 2t^2 + 3t - 2$. The induced power in the coil at time $t = 3 \ s$ is (in $W$)

$A$ conducting circular loop of resistance $20 \Omega$ and cross-sectional area $20 \times 10^{-2} \,m^{2}$ is placed perpendicular to a spatially uniform magnetic field $B$, which varies with time $t$ as $B = 2 \sin(50 \pi t) \,T$. Find the net charge flowing through the loop in $20 \,ms$ starting from $t = 0$. (in $\,C$)

As shown in the figure,$P$ and $Q$ are two coaxial conducting loops separated by some distance. When the switch $S$ is closed,a clockwise current $I_P$ flows in $P$ (as seen by $E$) and an induced current $I_{Q_1}$ flows in $Q$. The switch remains closed for a long time. When $S$ is opened,a current $I_{Q_2}$ flows in $Q$. Then the directions of $I_{Q_1}$ and $I_{Q_2}$ (as seen by $E$) are:

$A$ wire loop is placed in a region of time-varying magnetic field which is oriented orthogonally to the plane of the loop as shown in the figure. The graph shows the magnetic field variation as a function of time. Assume the positive $emf$ is the one which drives a current in the clockwise direction as seen by the observer in the direction of $B$. Which of the following graphs best represents the induced $emf$ as a function of time?