$A$ circular coil of radius $r$ is placed on another circular coil whose radius is $R$. The current flowing through the larger coil is changing, and their centers coincide. Given $R \gg r$, if both coils are coplanar, then the mutual inductance between them is proportional to:

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:

In an induction coil,the secondary $e.m.f.$ is

There are two long coaxial solenoids of the same length $l$. The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self-inductance of the inner coil is

An alternating current with an angular frequency of $\omega = 200\,rad/s$ and a peak value of $I_0 = 1\,A$,as shown in the figure,is applied to the primary coil of a transformer. If the coefficient of mutual induction between the primary and the secondary coils is $M = 1.5\,H$,the magnitude of the induced voltage in the secondary coil will be.....$V$.

Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .