Write formula for mutual inductance for two very long coaxial solenoids of length $\mathrm{l}$.

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_______.

With the decrease of current in the primary coil from $2\,amperes$ to zero value in $0.01\,s$ the $emf$ generated in the secondary coil is $1000\,volts$. The mutual inductance of the two coils is......$H$

An alternating current of frequency $200\,rad/sec$ and peak value $1\,A$ as shown in the figure, is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is $1.5\, H$, the voltage induced in the secondary will be.....$V$

The mutual inductance of an induction coil is $5\,H$. In the primary coil, the current reduces from $5\,A$ to zero in ${10^{ - 3}}\,s$. What is the induced emf in the secondary coil......$V$

The mutual inductance of a pair of coils, each of $N\,turns$, is $M\,henry$. If a current of $I\, ampere$ in one of the coils is brought to zero in $t$ $second$ , the $emf$ induced per turn in the other coil, in volt, will be