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).

An alternating current of angular frequency $\omega = 200 \, rad/sec$ and peak value $I_0 = 1 \, A$,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 coil is $M = 1.5 \, H$,the magnitude of the induced voltage in the secondary coil will be.....$V$.

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then:

$A$ circular loop of radius $0.3 \ cm$ lies parallel to a much bigger circular loop of radius $20 \ cm$. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is $15 \ cm$. If a current of $2.0 \ A$ flows through the smaller loop,then the flux linked with the bigger loop is $............. \times 10^{-11} \ Wb$.

$A$ circular current loop of radius $R$ is placed inside a square loop of side length $L$ $(L >> R)$ such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between the circular loop and the square loop is . . . . . . .

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ($\mu_0 =$ permeability of free space) (Both coils have single turn).