Two coils have a mutual inductance of $0.005 \text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 60\pi \text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil in volt will be (in $\pi$)

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L > l)$. If the loops are coplanar and their centers 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 small loop is on the axis of the bigger loop. The distance between their centres is $15 \, cm$. If a current of $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is:

There are $10$ turns in coil $M$ and $15$ turns in coil $N$. If a current of $2\ A$ is passed through coil $M$,then the flux linked with coil $N$ is $1.8 \times 10^{-3}\ Wb$. If a current of $3\ A$ is passed through coil $N$,then the flux linked with coil $M$ is:

$A$ pair of adjacent coils have a mutual inductance, $M$. The current in one coil changes from $0 \,A$ to $16 \,A$ in $0.3 \,s$, and the change of flux linkage with the other coil is $40 \,Wb$. The value of $M$ is: (in $\,H$)

Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).