When a current of $4 \,A$ changes to $8 \,A$ in $0.6 \,s$ in a primary coil, it induces an e.m.f. of $50 \,mV$ in the secondary coil. The mutual inductance between the two coils is: (in $\,mH$)

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

Two circular coils of radii $r_1$ and $r_2$ $(r_1 \ll r_2)$ are placed coaxially with their centers coinciding. The mutual inductance of the arrangement 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 induction of the arrangement is (Both coils have single turn,$\mu_0 =$ permeability of free space).

Two coils $P$ and $Q$ are separated by some distance. When a current of $3\, A$ flows through coil $P$,a magnetic flux of $10^{-3}\, Wb$ passes through $Q$. No current is passed through $Q$. When no current passes through $P$ and a current of $2\, A$ passes through $Q$,the flux through $P$ is:

$A$ solenoid of length $60 \ cm$ with $15$ turns per $cm$ and area of cross-section $4 \times 10^{-3} \ m^2$ completely surrounds another co-axial solenoid of the same length and area of cross-section $2 \times 10^{-3} \ m^2$ with $40$ turns per $cm$. The mutual inductance of the system is: (in $mH$)