The current $i$ in an induction coil varies with time $t$ according to the graph shown. Which of the following graphs shows the induced $emf$ $(e)$ in the coil with time?

In the figure,the switch $S$ is closed so that a current flows in the iron-core inductor which has inductance $L$ and the resistance $R$. When the switch is opened,a spark is obtained at the contacts. The spark is due to

$A$ flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure. The graph of induced $emf$ in the coil is represented by

$(a)$ $A$ closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets?
$(b)$ $A$ closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop
$\quad (i)$ when it is wholly inside the region between the capacitor plates
$\quad (ii)$ when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop.
$(c)$ $A$ rectangular loop and a circular loop are moving out of a uniform magnetic field region to a field-free region with a constant velocity $v$. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops.
$(d)$ Predict the polarity of the capacitor in the situation described by the figure.

$A$ 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 $\,C$)

An electron moves along the line $AB$,which lies in the same plane as a circular loop of conducting wires as shown in the diagram. What will be the direction of current induced,if any,in the loop?