$A$ small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side $L$ $(L \gg \ell)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{-7} \text{ H}$, where $x = \dots$

Two coils are kept near each other. When no current passes through the first coil and the current in the $2^{nd}$ coil increases at the rate of $10 \,A/s$, the e.m.f. in the $1^{st}$ coil is $20 \,mV$. When no current passes through the $2^{nd}$ coil and $3.6 \,A$ current passes through the $1^{st}$ coil, the flux linkage in coil $2$ is:

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

Two conducting circular loops of radii $R_{1}$ and $R_{2}$ are placed in the same plane with their centres coinciding. If $R_{1} >> R_{2}$,the mutual inductance $M$ between them will be directly proportional to:

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is:

The mutual inductance between two coils is $1.25 \ H$. If the current in the primary coil changes at the rate of $80 \ A/s$, then the induced $e.m.f.$ in the secondary coil is ...... $V$.