Two coils have a mutual inductance of $0.005\,H$. The current in the first coil changes 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 $emf$ in the second coil will be: (in $\pi \,V$)

$A$ coil of radius $r$ is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide. $(R \gg r)$ If both the coils are coplanar,then the mutual inductance between them 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

Two coils have a mutual inductance of $0.004 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 50 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil in volt is (in $\pi$)

$A$ 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:

In a transformer, the coefficient of mutual inductance between the primary and the secondary coil is $0.2 \, H$. When the current changes by $5 \, A/s$ in the primary, the induced $e.m.f.$ in the secondary will be......$V$