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

A pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s ,$ what is the change of flux (in $Wb$) linkage with the other coil?

Two coils of self inductance ${L_1}$ and ${L_2}$ are placed closer to each other so that total flux in one coil is completely linked with other. If $M$ is mutual inductance between them, then $M$ is

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 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 ........... $V$

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