What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times {10^{ - 2}}\,Wb$ and change in current is $0.01\,A$......$henry$

Two coils have mutual inductance $0.002 \ \mathrm{H}$. The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$, where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ $\mathrm{rad} / \mathrm{s}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi}{\alpha} \mathrm{V}$. The value of $\alpha$ is_______.

Explain mutual induction and derive equation of mutual $\mathrm{emf}$.

A pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s ,$ what is the change of flux (in $Wb$) linkage with the other coil?

What is the mutual inductance of a two-loop system as shown with centre separation l

The mutual inductance between the rectangular loop and the long straight wire as shown in figure is $M$.