A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is,

Net magnetic field at point 'P'

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

Here $\overrightarrow{{\mathrm{B}}_1}\text{ and }\overrightarrow{{\mathrm{B}}_2}$ are equal in magnitude and opposite in direction.

Hence,$B_{net}=B_1-B_2$

${\mathrm{i}}_1=\mathrm{i}\left(\frac{\mathrm{\theta }}{2\mathrm{\pi }}\right)\Rightarrow {\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_1}{2\mathrm{R}}\left(\frac{2\mathrm{\pi }-\mathrm{\theta }}{2\mathrm{\pi }}\right)$

${\mathrm{i}}_2=\mathrm{i}\left(\frac{2\mathrm{\pi }-\mathrm{\theta }}{2\mathrm{\pi }}\right)\Rightarrow {\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_2}{2\mathrm{R}}\left(\frac{\mathrm{\theta }}{2\mathrm{\pi }}\right)$

${\mathrm{B}}_{\mathrm{net}}={\mathrm{B}}_1-{\mathrm{B}}_2=0$