A small square loop of wire of side $l$ is placed inside a large circular loops of radius $r$. The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to

A circular loop ofradius $0.3\ cm$ lies parallel to amuch bigger circular loop ofradius $20\ cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15\ cm$. If a current of $2.0\ A$ flows through the smaller loop, then the flux linked with bigger loop is

The number of turns of primary and secondary coils of a transformer are $5$ and $10$ respectively and the mutual inductance of the transformer is $25\,henry$. Now the number of turns in the primary and secondary of the transformer are made $10$ and $5$  respectively. The mutual inductance of the transformer in henry will be

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

A coil of radius $1\, cm$ and of turns $100$ is placed in the middle of a long solenoid of  radius $5\, cm$. and having $5\, turns/cm$. parallel to the axis of solenoid The mutual  inductance in millihenery will be