The coefficient of mutual inductance,when magnetic flux changes by $2 \times 10^{-2} \ Wb$ and current changes by $0.01 \ A$,is ... $H$.

$A$ circular wire loop of radius $R$ is placed in the $x$-$y$ plane centered at the origin $O$. $A$ square loop of side $a$ $(a \ll R)$ having two turns is placed with its center at $z = \sqrt{3} R$ along the axis of the circular wire loop,as shown in the figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the $z$-axis. If the mutual inductance between the loops is given by $\frac{\mu_0 a^2}{2^{p / 2} R}$,then the value of $p$ is

The coefficient of mutual induction is $2 \text{ H}$ and the induced e.m.f. across the secondary is $2 \text{ kV}$. The current in the primary is reduced from $6 \text{ A}$ to $3 \text{ A}$. The time required for the change of current is:

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

$A$ current $I = 10 \sin(100 \pi t) \text{ A}$ is passed in a coil, which induces a maximum emf of $5 \pi \text{ V}$ in a neighboring coil. The mutual inductance of the two coils is: (in $\text{ mH}$)

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then: