Two different coils of self-inductance $L_{1}$ and $L_{2}$ are placed close to each other so that the effective flux in one coil is completely linked with the other. If $M$ is the mutual inductance between them,then:

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

$A$ solenoid of length $60 \ cm$ with $15$ turns per $cm$ and area of cross-section $4 \times 10^{-3} \ m^2$ completely surrounds another co-axial solenoid of the same length and area of cross-section $2 \times 10^{-3} \ m^2$ with $40$ turns per $cm$. The mutual inductance of the system is: (in $mH$)

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

Two concentric coplanar circular conducting loops have radii $R$ and $r$ $(R \gg r)$. Their mutual inductance is proportional to

$A$ square loop of side length $a$ is moving away from an infinitely long current-carrying conductor at a constant speed $v$ as shown. Let $x$ be the instantaneous distance between the long conductor and side $AB$. The mutual inductance $M$ of the square loop-long conductor pair changes with time $t$ according to which of the following graphs?