In $SI$, Henry is the unit of

Two circuits have coefficient of mutual induction of $0.09$ $henry$. Average $e.m.f$. induced in the secondary by a change of current from $0$ to $20$ $ampere$ in $0.006$ $second$ in the primary will be......$V$

Two coils of self inductance $2\,\,mH$ and $8\,\,mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$  mH$

A circular loop of radius $0.3\, cm$ lies parallel to a much bigger circular loop of radius $20 \,cm$. The centre of the small loop on the axis of the bigger loop. The distance between their centres is $15\, cm$. If a current of $20\, A$ flows through the smaller loop, then the flux linked with bigger loop is

Write formula for mutual inductance for two very long coaxial solenoids of length $\mathrm{l}$.

A circular wire loop of radius $R$ is placed in the $x$-y plane centered at the origin $O. A$ square loop os side $a ( a << R$ ) having two turns is placed with its center at $a=\sqrt{3} \ R$ along the axis of the circular wire loop, as shown in 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