$A$ long straight wire carrying current $I$ and a rectangular frame with side lengths $a$ and $b$ lie in the same plane as shown in the figure. The mutual inductance of the wire and frame is

Two coils of wire $A$ and $B$ are placed mutually perpendicular as shown in the figure. When the current is changed in any one coil:

Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

With the decrease of current in the primary coil from $2\,A$ to zero in $0.01\,s$,the $emf$ generated in the secondary coil is $1000\,V$. The mutual inductance of the two coils is......$H$.

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,$\pi^2=10$).

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