In the current carrying conductor shown in figure, the magnetic induction at the centre O, of the semicircular part is

• A

  $\left(2+\frac{1}{\mathrm{\pi }}\right)\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{i}}{2\mathrm{R}}$

• B

  $\left(1+\frac{2}{\mathrm{\pi }}\right)\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{i}}{2\mathrm{R}}$

• C

  $\left(1+\frac{1}{\mathrm{\pi }}\right)\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{i}}{2\mathrm{R}}$

• D

  $\left(1-\frac{1}{\mathrm{\pi }}\right)\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{i}}{2\mathrm{R}}$