Mutual inductance of two coils can be increased by

If a change in current of $0.01 \,A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} \,Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $\,H$)

$A$ small coil of radius $r$ is placed at the centre of a large coil of radius $R$,where $R >> r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

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:

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. $= 50 \text{ Hz}$)

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then: