Physics - Magnetism Question with Solution | TestHub

Field due to section 1

${\overrightarrow{B}}_1=\frac{{\mu }_{0}i}{4\pi R}$upwards

field due to section 2

${\overrightarrow{B}}_2=\frac{{\mu }_{0}i\left(\pi \right)}{4\pi R}=\frac{{\mu }_{0}i}{4R}$upwards

Field due to section 3

${\overrightarrow{B}}_3=\frac{{\mu }_{0}i}{4\pi R}$upwards

therefore

${\overrightarrow{B}}_{net}={\overrightarrow{B}}_1+{\overrightarrow{B}}_2+{\overrightarrow{B}}_3$upwards

${\overrightarrow{B}}_{net}=\frac{{\mu }_{0}i}{4\pi R}+\frac{{\mu }_{0}i}{4R}+\frac{{\mu }_{0}i}{4\pi R}$upwards

${\overrightarrow{B}}_{net}=\frac{{\mu }_{0}i}{4R}\left(\frac{2}{\pi }+1\right)$upwards