Physics - Magnetism Question with Solution | TestHub

The perpendicular distance of centroid from any side,$\frac{1}{2\sqrt{3}}\mathrm{ }\mathrm{m}$
Magnetic field due to one side.
${\mathrm{B}}_1=\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{4\mathrm{\pi }\mathrm{r}}[\mathrm{c}\mathrm{o}\mathrm{s}{\mathrm{\theta }}_1+\mathrm{c}\mathrm{o}\mathrm{s}{\mathrm{\theta }}_2]$
$=\frac{{\mathrm{\mu }}_0\left(10\right)}{4\mathrm{\pi }\mathrm{r}\left(\frac{1}{2\sqrt{3}}\right)}\left[\mathrm{c}\mathrm{o}\mathrm{s}{30}^{°}+\mathrm{c}\mathrm{o}\mathrm{s}{30}^{°}\right]$
$=\frac{5\sqrt{3}}{\mathrm{\pi }\mathrm{ }}{\mathrm{\mu }}_0\mathrm{ }\left[\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}\right]=\frac{15{\mathrm{\mu }}_0}{\mathrm{\pi }}$
Net magnetic field$\mathrm{B}=3{\mathrm{B}}_1=\frac{45}{\mathrm{\pi }}{\mathrm{\mu }}_0=\frac{45}{\mathrm{\pi }}\times 4\pi \times {10}^{-7}$
$=180\times {10}^{-7}\mathrm{ }\mathrm{T}$
$=18\mathrm{ }\mathrm{\mu }\mathrm{T}$