Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

Two coils of self-inductances $2\, mH$ and $8\, mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$mH$.

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 induction of the arrangement is (Both coils have single turn,$\mu_0 =$ permeability of free space).

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 $\mu_0 = 4\pi \times 10^{-7} \ T \ m \ A^{-1}$):

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is:

Two coils of self-inductance ${L_1}$ and ${L_2}$ are placed close to each other so that the total flux in one coil is completely linked with the other. If $M$ is the mutual inductance between them,then $M$ is: