$A$ current $I = 10 \sin(100 \pi t) \text{ A}$ is passed in a coil, which induces a maximum emf of $5 \pi \text{ V}$ in a neighboring coil. The mutual inductance of the two coils is: (in $\text{ mH}$)

$A$ 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

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a$ $(a \ll R)$ is bent in the form of a square. The two loops are then placed in the same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows from $'c'$ to $'d'$ in loop $(2)$. In an experiment,the graph of $i_2$ against time $'t'$ is as shown below. Which one$(s)$ of the following graphs could have caused $i_2$ to behave as given above?

Two concentric circular coils,one of small radius $r_1$ and the other of large radius $r_2$,such that $r_1 \ll r_2$,are placed coaxially with centers coinciding. Obtain the mutual inductance of the arrangement.

Two coils have a mutual inductance of $0.004 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 50 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil in volt is (in $\pi$)