The mutual inductance $(M)$ of two coils is $3 \ H$. The self-inductances of the coils are $4 \ H$ and $9 \ H$ respectively. The coefficient of coupling between the coils is

The induction coil works on the principle of

Derive the formula for mutual inductance of two very long coaxial solenoids. Also,discuss the reciprocity theorem.

Two concentric circular coils,one of small radius $r_1$ and the other of large radius $r_2$,such that $r_1 \ll r_2$,are placed co-axially with their centres coinciding. The mutual inductance $M$ of the arrangement is proportional to . . . . . . .

$A$ small square loop of side $a$ and one turn is placed inside a larger square loop of side $b$ and one turn $(b \gg a)$. The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side $b$,then the coefficient of mutual inductance between the two loops is

Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .