The mutual inductance of two coils is $8 \ mH$. The current in one coil changes according to the equation $I = 12 \sin 100t$,where $I$ is in ampere and $t$ is time in second. The maximum value of emf induced in the second coil is (in $V$)

$X$ and $Y$ are two metallic coils arranged in such a way that when the steady change in current flowing in coil $X$ is $4 \ A$,the change in magnetic flux associated with coil $Y$ is $0.4 \ Wb$. The mutual inductance of the system of these coils is . . . . . . $H$.

$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire $L$ $(L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in the figure. The mutual inductance of the system 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 inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

$A$ 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 have a mutual inductance of $0.005 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 100 \pi \ rad/s$. The maximum value of the induced emf in the second coil is: