$A$ 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?

$A$ circular loop of radius $0.3 \, cm$ lies parallel to a much bigger circular loop of radius $20 \, cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15 \, cm$. If a current of $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is:

$A$ long solenoid '$S$' has 'n' turns per meter,with diameter 'a'. At the centre of this coil we place a smaller coil of '$N$' turns and diameter 'b' (where $b < a$). If the current in the solenoid increases linearly with time,what is the induced emf appearing in the smaller coil? Plot a graph showing the nature of variation in emf,if current varies as a function of $I(t) = mt^2 + C$.

Two coils have a mutual inductance $0.005 \, H$. 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 $e.m.f.$ in the second coil is:

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 $emf$ induced (in $volt$) in the secondary coil is

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