Physics - Magnetism Question with Solution | TestHub

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

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

$=\frac{{\mu }_{0}i}{4\pi \left(3r\right)}\times \frac{\pi }{2}+\frac{{\mu }_{0}i}{4\pi \left(r\right)}\times \left(\frac{3\pi }{2}\right)$

$=\frac{{\mu }_{o}i}{8r}\left[\frac{1}{3}+3\right]$

$=\frac{5{\mu }_{o}i}{12r}$ acting downwards