If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times {10^{ - 2}}\,Wb$ in the other coil, then the mutual inductance of the two coils in henries is.....$H$

Two coils of self inductance ${L_1}$ and ${L_2}$ are placed closer to each other so that total flux in one coil is completely linked with other. If $M$ is mutual inductance between them, then $M$ is

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.

Two coils have mutual inductance $0.002 \ \mathrm{H}$. The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$, where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ $\mathrm{rad} / \mathrm{s}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi}{\alpha} \mathrm{V}$. The value of $\alpha$ is_______.

$(a)$ Obtain an expression for the mutual inductance between a long straight wire and a square loop of side $a$ as shown in Figure.

$(b)$ Now assume that the straight wire carries a current of $50\; A$ and the loop is moved to the right with a constant velocity, $v=10 \;m / s$ Calculate the induced $emf$ in the loop at the instant when $x=0.2\; m$ Take $a=0.1\; m$ and assume that the loop has a large resistance.

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.....$H$