The magnetic induction at the centre O in the figure shown is

In the following figure, magnetic fields at O due to sections 1, 2, 3 and 4 are considered as B₁ , B₂, B₃ and B₄, respectively.

B₁ = B₃ = 0

$\begin{array}{l}{\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}.\frac{\mathrm{\pi }}{{\mathrm{R}}_1}\otimes \\ {\mathrm{B}}_4=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}.\frac{\mathrm{\pi i}}{{\mathrm{R}}_2}\odot \\ \mathrm{As}\left|{\mathrm{B}}_2\right|>\left|{\mathrm{B}}_4\right|\\ \mathrm{So}{\mathrm{B}}_{\mathrm{net}}={\mathrm{B}}_2-{\mathrm{B}}_4\Rightarrow {\mathrm{B}}_{\mathrm{net}}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right)\otimes \end{array}$