$A$ very long straight conductor and an isosceles triangular conductor lie in a plane and are separated from each other as shown in the figure. If $a = 10 \ cm$,$b = 20 \ cm$,and $h = 10 \ cm$,find the coefficient of mutual induction.

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?

$A$ 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 $\text{ mH}$)

Two circuits have a mutual inductance of $0.1\, H$. What average $e.m.f.$ is induced in one circuit when the current in the other circuit changes from $0$ to $20\, A$ in $0.02\, s$ (in $, V$)?

Two coils,$X$ and $Y$,are kept in close vicinity of each other. When a varying current,$I(t)$,flows through coil $X$,the induced emf $(V(t))$ in coil $Y$ varies in the manner shown in the figure. The variation of $I(t)$ with time can then be represented by the graph labeled as:

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is: