$A$ transformer works on the principle of

Two coils have a mutual inductance of $ 0.005 \ H $. The current changes in the first coil according to the equation $ i = i_{m} \sin \omega t $,where $ i_{m} = 10 \ A $ and $ \omega = 100 \pi \ rad \ s^{-1} $. The maximum value of the emf induced in the second coil is:

$A$ circular loop of radius $0.3 \ cm$ lies parallel to a much bigger circular loop of radius $20 \ cm$. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is $15 \ cm$. If a current of $2.0 \ A$ flows through the smaller loop,then the flux linked with the bigger loop is $............. \times 10^{-11} \ Wb$.

$A$ varying current at the rate of $3 \, A/s$ in a coil generates an $e.m.f.$ of $8 \, mV$ in a nearby coil. The mutual inductance of the two coils is:

$AB$ 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 $PQRS$.

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :