Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2$,the mutual inductance $M$ between them will be directly proportional to

$A$ circular loop of radius $0.3 \, cm$ lies parallel to a much bigger circular loop of radius $20 \, cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15 \, cm$. If a current of $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is:

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a$ $(a \ll R)$ is bent in the form of a square. The two loops are then placed in the same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?

$A$ solenoid of length $60 \ cm$ with $15$ turns per $cm$ and area of cross-section $4 \times 10^{-3} \ m^2$ completely surrounds another co-axial solenoid of the same length and area of cross-section $2 \times 10^{-3} \ m^2$ with $40$ turns per $cm$. The mutual inductance of the system is: (in $mH$)

$O$ is the centre of two coplanar concentric circular conductors,$A$ and $B$,of radii $r$ and $R$ respectively as shown in the figure. Here $r \ll R$. The mutual inductance of the system of the conductors can be given by . . . . . . .

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows from $'c'$ to $'d'$ in loop $(2)$. In an experiment,the graph of $i_2$ against time $'t'$ is as shown below. Which one$(s)$ of the following graphs could have caused $i_2$ to behave as given above?