$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $(L > l)$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

$A$ short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long,coaxial solenoid (length $L$,radius $R$ and $N$ turns per unit length,with $R > r$). Current $I$ flows in the short solenoid. Choose the correct statement.

Two coils are kept near each other. When no current passes through the first coil and the current in the $2^{nd}$ coil increases at the rate of $10 \,A/s$, the e.m.f. in the $1^{st}$ coil is $20 \,mV$. When no current passes through the $2^{nd}$ coil and $3.6 \,A$ current passes through the $1^{st}$ coil, the flux linkage in coil $2$ is:

$A$ pair of adjacent coils has a mutual inductance of $2 \text{H}$. If the current in one coil changes from $0 \text{A}$ to $30 \text{A}$ in $0.15 \text{s}$,what is the change of flux linkage with the other coil (in $\text{ Wb}$)?

$X$ and $Y$ are two metallic coils arranged in such a way that when the steady change in current flowing in coil $X$ is $4 \ A$,the change in magnetic flux associated with coil $Y$ is $0.4 \ Wb$. The mutual inductance of the system of these coils is . . . . . . $H$.

$AB$ is an infinitely long wire placed in the plane of a rectangular coil $PQRS$ with dimensions as shown in the figure. Calculate the mutual inductance of wire $AB$ and coil $PQRS$.