$A$ 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 :

Two coils have a mutual inductance $5 \times 10^{-3} \text{ H}$. The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 100 \pi \text{ rad/s}$. What is the value of the maximum e.m.f. in the second coil (in $\pi \text{ V}$)?

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:

Explain mutual induction and derive the equation for mutual $emf$.

$A$ varying current at the rate of $3 \, A/s$ in a coil generates an $e.m.f.$ of $8 \, mV$ in a nearby coil. The mutual inductance of the two coils is:

Two concentric circular coils,one of small radius $r$ and the other of large radius $R$,are placed coaxially with their centers coinciding. If the radius $r$ is changed by $2 \%$,then the change in mutual inductance of the arrangement is (assume $r \ll R$). (in $\%$)