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 =___

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.......$mV$

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.....$millihenry$

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....$H$

In a $dc$ motor, induced $e.m.f.$ will be maximum

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