Two conducting circular loops $A $and $B$ are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them $1$s:

Write formula for mutual inductance for two very long coaxial solenoids of length $\mathrm{l}$.

Mutual inductance of two coils can be increased by

Two coils $X$ and $Y$ are placed in a circuit such that when a current changes $2A$ in coil $X,$ the magnetic flux changes by $0.4\,weber$ in $Y$. The value of mutual inductance of the coils....$H$

A solenoid has $2000$ turns wound over a length of $0.3\,m$. The area of cross-section is $1.2\times10^{-3}\,m^2$. Around its central section a coil of $300$ turns is closely wound. If an initial current of $1\,A$ is reversed in $0.25\,s$. Find the emf induced in the coil.......$mV$

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 =___