Two coils $P$ and $S$ have a mutual inductance of $3 \times 10^{-3} \ H$. If the current in the coil $P$ is $I = 20 \sin(50 \pi t) \ A$,then the maximum value of the e.m.f. induced in coil $S$ is (in $V$)

Two coils have a mutual inductance of $0.005 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 100 \pi \ rad/s$. The maximum value of the induced emf in the second coil is:

The coefficient of mutual inductance between the primary and the secondary coil of a transformer is $0.2 H$. When the current in the primary coil changes at a rate of $5 A s^{-1}$,the induced emf in the secondary coil will be: (in $V$)

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

Mutual inductance of two coils can be increased by

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