The magnitude of magnetic field at $O$ (Centre of the circular part) of the current carrying coil as shown is 

$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying current $i_1$ and $i_2$, respectively as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the flux densities at $O$ due to $A$ and $B$ is $1:3$, then the value of $\frac{i_1}{i_2}$ will be

A linear small part of a circuit $PQ$ is situated on $x$ axis from $x=-\frac{a}{2}$ to $x=+\frac{a}{2}$ and a current $I$ is flowing through it. The magnetic field produced due to part $PQ$ at point $x=+a$ will be