Two concentric circular coils with radii $1\,cm$ and $1000\,cm$,and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be $.........\times 10^{-8}\,H$ (Take,$\pi^2=10$).

Two planar concentric rings of metal wire having radii $r_1$ and $r_2$ $(r_1 > r_2)$ 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).

$A$ coil of radius $r$ is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide. $(R \gg r)$ If both the coils are coplanar,then the mutual inductance between them is proportional to

Alternating current of peak value $(\frac{2}{\pi}) \ A$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coil is $1 \ H$. The peak e.m.f. induced in the secondary coil is (Frequency of a.c. $= 50 \ Hz$) (in $V$)

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:

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is: