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$

A small square loop of wire of side $l$ is placed inside a large circular loops of radius $r$. The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to

A short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length $L$, radius $R$ and $N$ turns per unit length, with $R>r$ ). Current $I$ follows in the short solenoid. Choose the correct statement.

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 of self inductances $2\, mH$ and $8\, mH$ Hare placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$mH$

Derive formula for mutual inductance for two very long coaxial solenoids. Also discuss reciprocity theorem.