Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil $Q$ at the rate of $10 \ A/s$,the e.m.f. in coil $P$ is $15 \ mV$. When coil $Q$ carries no current and current of $1.8 \ A$ flows through coil $P$,the magnetic flux linked with coil $Q$ is (in $mWb$)

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

$A$ coil of radius $r$ is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide. $(R \gg r)$ If both the coils are coplanar,then the mutual inductance between them is proportional to

$A$ 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 $I(t) = mt^2 + C$.

$A$ coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current flowing through it is changing) so that their centres coincide $(R \gg r)$. If both the coils are coplanar,then the mutual inductance between them is $(\mu_0 = \text{permeability of free space})$

Write the formula for the mutual inductance of two very long coaxial solenoids of length $l$.