Two circular coils have their centers at the same point. The mutual inductance between them will be maximum when their axes

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. $= 50 \text{ Hz}$)

In a pair of adjacent coils,if the current in one coil changes from $10 \,A$ to $2 \,A$ in a time $0.2 \,s$,an emf of $120 \,V$ is induced in the other coil. The mutual inductance of the pair of coils is: (in $\,H$)

$A$ circular current loop of radius $R$ is placed inside a square loop of side length $L$ $(L >> R)$ such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between the circular loop and the square loop is . . . . . . .

Explain mutual induction and derive the equation for mutual $emf$.

When magnetic flux changes from $6.5 \times 10^{-2} \ Wb$ to $11 \times 10^{-2} \ Wb$ and the change in current is $0.03 \ A$,the coefficient of mutual inductance will be: (in $H$)