Two coils have a mutual inductance $0.005\,H$ . The current changes in the first coil 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 $emf$ in the second coil will be

$AB$ is an infinitely long wire placed in the plane of rectangular coil of dimensions as shown in the figure. Calculate the mutual inductance of wire $AB$ and coil $PQRS$

Two conducting circular loops of radii ${R_1}$ and ${R_2}$ are placed in the same plane with their centres coinciding. If ${R_1} > > {R_2}$, the mutual inductance $M$ between them will be directly proportional to

Two coaxial coils are very close to each other and their mutual inductance is $5 \,mH$. If a current $50 sin 500 \,t$ is passed in one of the coils then the peak value of induced e.m.f in the secondary coil will be ........... $V$

$A$ small coil of radius $r$ is placed at the centre of $a$ large coil of radius $R,$ where $R > > r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

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