Two coils of self-inductance $100\,mH$ and $400\,mH$ are placed very close to each other. Find the maximum mutual inductance between the two. (The current value is irrelevant to the calculation of mutual inductance).

$A$ small square loop of wire of side $l$ is placed inside a large circular loop of radius $r$. The loops are coplanar and their centers coincide. The mutual inductance of the system is proportional to

$AB$ 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 $PQRS$.

$A$ 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:

$A$ pair of adjacent coils have a mutual inductance, $M$. The current in one coil changes from $0 \,A$ to $16 \,A$ in $0.3 \,s$, and the change of flux linkage with the other coil is $40 \,Wb$. The value of $M$ is: (in $\,H$)

$A$ square loop of side length $a$ is moving away from an infinitely long current-carrying conductor at a constant speed $v$ as shown. Let $x$ be the instantaneous distance between the long conductor and side $AB$. The mutual inductance $M$ of the square loop-long conductor pair changes with time $t$ according to which of the following graphs?