$A$ 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

There are $10$ turns in coil $M$ and $15$ turns in coil $N$ . If a current of $2\ A$ is passed through coil $M$ then the flux linked with coil $N$ is $1.8 × 10^{-3}\ Wb$ . If a current of $3\ A$ is passed through coil $N$ then flux linked with coil $M$ is

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be

If the current $30 \,A$ flowing in the primary coil is made zero in $0.1 \,sec$. The $e.m.f.$ induced in the secondary coil is $1.5 \,volt$. The mutual inductance between the coil is.....$H$

The mutual inductance between a primary and secondary circuits is $0.5 \,H$. The resistances of the primary and the secondary circuits are $20\,\Omega$ and $5\,\Omega $ respectively. To generate a current of $0.4 \,A$ in the secondary, current in the primary must be changed at the rate of.....$A/s$