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_______.

Two circuits have coefficient of mutual induction of $0.09$ $henry$. Average $e.m.f$. induced in the secondary by a change of current from $0$ to $20$ $ampere$ in $0.006$ $second$ in the primary will be......$V$

If the current $30 \,A$ flowing in the primary coil is made zero in $0.1 \,sec$. The $e.m.f.$ induced in the secondary coil is $1.5 \,volt$. The mutual inductance between the coil is.....$H$

A coil of radius $1\, cm$ and of turns $100$ is placed in the middle of a long solenoid of  radius $5\, cm$. and having $5\, turns/cm$. parallel to the axis of solenoid The mutual  inductance in millihenery will be

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