$A$ circular coil of radius $r$ is placed on another circular coil whose radius is $R$. The current flowing through the larger coil is changing, and their centers coincide. Given $R \gg r$, if both coils are coplanar, then the mutual inductance between them is proportional to:

The mutual inductance between two coils is $1.25 \ H$. If the current in the primary coil changes at the rate of $80 \ A/s$, then the induced $e.m.f.$ in the secondary coil is ...... $V$.

$A$ small coil of radius $r$ is placed at the centre of a large coil of radius $R$,where $R >> r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

Two coaxial coils $A$ and $B$ of radii $R_{1}$ and $R_{2}$ are placed in the same plane $(R_{2} > R_{1})$. If a current is passed through coil $B$,the coefficient of mutual inductance between the coils is proportional to:

$A$ circular wire loop of radius $R$ is placed in the $x$-$y$ plane centered at the origin $O$. $A$ square loop of side $a$ $(a \ll R)$ having two turns is placed with its center at $z = \sqrt{3} R$ along the axis of the circular wire loop,as shown in the figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the $z$-axis. If the mutual inductance between the loops is given by $\frac{\mu_0 a^2}{2^{p / 2} R}$,then the value of $p$ is

Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil $Q$ at the rate $10 \ A/s$,the emf in coil $P$ is $12 \ mV$. When coil $Q$ carries no current and current of $1.5 \ A$ flows through coil $P$,the magnetic flux linked with the coil $Q$ in $mWb$ is