In the figure, two infinitely long wires carry equal currents $i$. Each follows a $90°$ arc on the circumference of the same circle of radius $R.$ Show that the magnetic field $\overrightarrow{B}$ at the Centre of the circle is the same as the field $\overrightarrow{B}$ at distance $R$ below an infinite straight wire carrying a current $i$ to the left.

Two concentric coplanar circular loops of radii $r_1$ and $r_2$ carry currents of $i_1$ and $i_2$, respectively, in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the Centre of the loops is half of that due to $i_1$ alone at the Centre. If $r_2=2r_1$, find the value of $\frac{i_2}{i_1}$.

A current $i$ ampere flows in a circular arc of wire whose radius is $R$, which subtend an angle $\frac{3\mathrm{\pi }}{2}$ radian at its Centre. The magnetic induction $B$ at the Centre is

In the figure shown, there are two semicircles of radii $r_1$ and $r_2$ in which a current $i$ is flowing. The magnetic induction at the Centre $O$ will be