What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times 10^{-2}\,Wb$ and change in current is $0.01\,A$......$ henry$

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

An $e.m.f.$ of $100\,millivolts$ is induced in a coil when the current in another nearby coil becomes $10\, ampere$ from zero in $0.1\,second$ . The coefficient of mutual induction between the two coils will be.....$millihenry$

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L(L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. 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 =___

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