$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :

$A$ circular loop of radius $0.3 \ cm$ lies parallel to a much bigger circular loop of radius $20 \ cm$. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is $15 \ cm$. If a current of $2.0 \ A$ flows through the smaller loop,then the flux linked with the bigger loop is $............. \times 10^{-11} \ Wb$.

$A$ coil of radius $1\, cm$ and $100$ turns is placed in the middle of a long solenoid of radius $5\, cm$ having $5\, turns/cm$, with its axis parallel to the axis of the solenoid. The mutual inductance in millihenry is:

Two coils of self-inductance ${L_1}$ and ${L_2}$ are placed close to each other so that the total flux in one coil is completely linked with the other. If $M$ is the mutual inductance between them,then $M$ is:

Two coils have a mutual inductance $0.005 \, H$. The current changes in the first coil according to the equation $I = I_0 \sin(\omega t)$,where $I_0 = 10 \, A$ and $\omega = 100\pi \, rad/s$. The maximum value of the $e.m.f.$ in the second coil is:

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: