$A$ small coil of radius $r$ is placed at the centre of $a$ large coil of radius $R,$ where $R > > r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

A circular wire loop of radius $R$ is placed in the $x$-y plane centered at the origin $O. A$ square loop os side $a ( a << R$ ) having two turns is placed with its center at $a=\sqrt{3} \ R$ along the axis of the circular wire loop, as shown in 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

Two coils have mutual inductance $0.002 \ \mathrm{H}$. The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$, where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ $\mathrm{rad} / \mathrm{s}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi}{\alpha} \mathrm{V}$. The value of $\alpha$ is_______.

A small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side $L$ $\left(\mathrm{L}=\ell^2\right)$. The loops are coplanar and therr centers coinside. The value of the mutual inductance of the system is $\sqrt{\mathrm{x}} \times 10^{-7} \mathrm{H}$, where X =___

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

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centre coinciding. If $R_1 >> R_2$ the mutual inductance $M$ between them will be directly proportional to