$A$ long straight wire carrying current $I$ and a rectangular frame with side lengths $a$ and $b$ lie in the same plane as shown in the figure. The mutual inductance of the wire and frame is

Two coils have a mutual inductance $5 \times 10^{-3} \text{ H}$. The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$, where $I_0 = 10 \text{ A}$ and $\omega = 100 \pi \text{ rad/s}$. What is the value of the maximum e.m.f. in the second coil (in $\pi \text{ V}$)?

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

The inductors of two $LR$ circuits are placed next to each other,as shown in the figure. The values of the self-inductance of the inductors,resistances,mutual-inductance,and applied voltages are specified in the given circuit. After both the switches are closed simultaneously,the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is . . . . $mJ$.

The induction coil works on the principle of

$A$ 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 the figure. The mutual inductance of the system is: