A straight conductor carrying current splits into two parts forming a circular loop as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre of the loop is:

When current $I$ enters a uniform circular loop and splits into two paths to exit, the magnetic field produced by the upper arc and lower arc at the center are in opposite directions.The magnetic field due to an arc subtending angle $\theta$ is $B=\frac{{\mu }_{0}i}{4\pi R}\theta$.For any split in a uniform wire loop, the ratio of currents is inversely proportional to the lengths (resistances).$I_1{L}_1=I_2{L}_2$ Since $L\propto \theta$, $I_1{\theta }_1=I_2{\theta }_2$.The magnitudes of magnetic fields $B_1$ and $B_2$ are proportional to $I_1{\theta }_1$ and $I_2{\theta }_2$.Thus, $B_1=B_2$. Since they are opposite in direction, the net magnetic field is zero.