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 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 $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other, on passing a current of $3.0$ ampere in $A$, the flux linked with A is $1.2 \times {10^{ - 4}}\,weber$ and with $B$ it is $9.0 \times {10^{ - 5}}\,weber$. The mutual inductance of the system 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 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 pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s ,$ what is the change of flux (in $Wb$) linkage with the other coil?