An $e.m.f.$ of $100 \, mV$ is induced in a coil when the current in another nearby coil changes from $0 \, A$ to $10 \, A$ in $0.1 \, s$. The coefficient of mutual induction between the two coils is . . . . . . $mH$.

$A$ 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 $............. \times 10^{-11} \ Wb$.

The mutual inductance between the rectangular loop and the long straight wire as shown in the figure is $M$.

The 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 $(\mu_0 = \text{permeability of free space})$

If a change in current of $0.01 \,A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} \,Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $\,H$)

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \ cm^2$ and length $\ell = 20 \ cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \ T \ m \ A^{-1}$):