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

There are two long co -axial solenoids of same length $l.$ The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self -inductance of the inner -coil is

The induction coil works on the principle of

Two conducting circular loops $A $and $B$ are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them $1$s:

In a transformer, the coefficient of mutual inductance between the primary and the secondary coil is $0.2 \,henry$. When the current changes by $5$ $ampere/second$ in the primary, the induced $e.m.f$. in the secondary will be......$V$

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_______.