A current i flows through a loop as shown in figure. The magnetic...

The angle, subtended by arc $DE$ at $O$ is $\dfrac{\pi}{2}$ and $FC$ at $O = \dfrac{3\pi}{2}$ the effective magnetic field at $O$ is

$B = {B}_{DE} + {B}_{FC}$

$= \dfrac{{μ}_{0}i}{4\pi\left(3r\right)} \times \dfrac{\pi}{2} + \dfrac{{μ}_{0}i}{4\pi \left( r\right)}$ $\times$\left(\dfrac{3\pi}{2}\right)$</p><p>$= \dfrac{{μ}_{o}i}{8r} \left[\dfrac{1}{3} +3\right]$</p><p>=\dfrac{5{μ}_{o}i}{12r}acting downwards</p>$