If a current of $3.0 \ A$ flowing in the primary coil is reduced to zero in $0.001 \ s$,then the induced $e.m.f.$ in the secondary coil is $15000 \ V$. The mutual inductance between the two coils is (in $H$):

The mutual inductance between two coils is $1.25 \ H$. If the current in the primary coil changes at the rate of $80 \ A/s$, then the induced $e.m.f.$ in the secondary coil is ...... $V$.

An alternating current of peak value $\left(\frac{2}{\pi}\right) \text{ A}$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coils is $1 \text{ H}$. What is the peak electromotive force (e.m.f.) induced in the secondary coil (in $\text{ V}$)? (Frequency of a.c. $= 50 \text{ Hz}$)

$A$ 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 $............. \times 10^{-11} \ Wb$.

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?

Mutual inductance of two coils can be increased by