$A$ transformer works on the principle of

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :

The device that does not work on the principle of mutual induction is

$A$ circular loop of radius $0.3 \ cm$ lies parallel to a much bigger circular loop of radius $20 \ cm$. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is $15 \ cm$. If a current of $2.0 \ A$ flows through the smaller loop,then the flux linked with the bigger loop is $............. \times 10^{-11} \ Wb$.

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ($\mu_0 =$ permeability of free space) (Both coils have single turn).

$A$ 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