Two coils of self-inductance $100\,mH$ and $400\,mH$ are placed very close to each other. Find the maximum mutual inductance between the two. (The current value is irrelevant to the calculation of mutual inductance).

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 $\pi$)

Two coils,$X$ and $Y$,are kept in close vicinity of each other. When a varying current,$I(t)$,flows through coil $X$,the induced emf $(V(t))$ in coil $Y$ varies in the manner shown in the figure. The variation of $I(t)$ with time can then be represented by the graph labeled as:

The mutual inductance of a system of two coils does not depend on . . . . . . .

Two planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1 > r_2$) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by ($\mu_0$ = permeability of free space)

$A$ small coil of radius $r$ is placed at the centre of a large coil of radius $R$,where $R >> r$. The coils are coplanar. The coefficient of mutual inductance between the coils is