Two coils have a mutual inductance of $0.005\,H$. The current in the first coil changes 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: (in $\pi \,V$)

Two coaxial coils $A$ and $B$ of radii $R_{1}$ and $R_{2}$ are placed in the same plane $(R_{2} > R_{1})$. If a current is passed through coil $B$,the coefficient of mutual inductance between the coils is proportional to:

Give two definitions of mutual inductance, give its units and write factors on which its value depends.

An $e.m.f.$ of $100 \, mV$ is induced in a coil when the current in another nearby coil changes from $0 \, A$ to $10 \, A$ in $0.1 \, s$. The coefficient of mutual induction between the two coils is . . . . . . $mH$.

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

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: