There are two long co -axial solenoids of same length $l.$ The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self -inductance of the inner -coil is

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.....$H$

If the coefficient of mutual induction of the primary and secondary coils of an induction coil is $5\, H$ and a current of $10\, A$ is cut off in $5\times10^{-4}\, s$, the $emf$ inducted (in $volt$) in the secondary coil is

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

The mutual inductance between two coils is $1.25$ $henry$. If the current in the primary changes at the rate of $80$ $ampere/second,$ then the induced $e.m.f$ in the secondary is......$V$

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon