Two concentric coplanar circular conducting loops have radii $R$ and $r$ $(R \gg r)$. Their mutual inductance is proportional to

Two coils $X$ and $Y$ are placed in a circuit such that when a current changes by $2 \ A$ in coil $X$,the magnetic flux changes by $0.4 \ Wb$ in coil $Y$. The value of mutual inductance of the coils is .... $H$.

Two coils are kept near each other. When no current passes through the first coil and the current in the $2^{nd}$ coil increases at the rate of $10 \,A/s$, the e.m.f. in the $1^{st}$ coil is $20 \,mV$. When no current passes through the $2^{nd}$ coil and $3.6 \,A$ current passes through the $1^{st}$ coil, the flux linkage in coil $2$ is:

Two coils have a mutual inductance of $0.01 \ H$. The current in the first coil changes according to the equation $I = 5 \sin(200 \pi t)$. The maximum value of the e.m.f. induced in the second coil 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 $I(t) = mt^2 + C$.

$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is