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

Explain mutual induction and derive equation of mutual $\mathrm{emf}$.

$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

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.

Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other, on passing a current of $3.0$ ampere in $A$, the flux linked with A is $1.2 \times {10^{ - 4}}\,weber$ and with $B$ it is $9.0 \times {10^{ - 5}}\,weber$. The mutual inductance of the system is

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $(L > l)$. The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to