$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

$A$ 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

Give two definitions of mutual inductance, give its units and write factors on which its value depends.

The mutual inductance of an induction coil is $5\,H$. In the primary coil, the current reduces from $5\,A$ to zero in ${10^{ - 3}}\,s$. What is the induced emf in the secondary coil......$V$

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 of self inductances $2\, mH$ and $8\, mH$ Hare placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$mH$