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

The mutual inductance between the rectangular loop and the long straight wire as shown in figure is $M$.

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

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 are placed close to each other. The mutual inductance of the pair of coils depends upon

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