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 in $V$?

The mutual inductance $(M)$ of two coils is $3 \ H$. The self-inductances of the coils are $4 \ H$ and $9 \ H$ respectively. The coefficient of coupling between the coils is

The mutual inductance of a system of two coils does not depend on . . . . . . .

The mutual inductance between a primary and secondary circuit is $0.5 \, H$. The resistances of the primary and the secondary circuits are $20 \, \Omega$ and $5 \, \Omega$ respectively. To generate a current of $0.4 \, A$ in the secondary,the current in the primary must be changed at the rate of . . . . . . $A/s$.

An $e.m.f.$ of $100 \, mV$ is induced in a coil when the current in another nearby coil changes from $0 \, A$ to $10 \, A$ in $0.1 \, s$. The coefficient of mutual induction between the two coils is . . . . . . $mH$.

Write the formula for the mutual inductance of two very long coaxial solenoids of length $l$.