In the figure shown there are two semicircles of radii ${\text{r}}_{\text{1}}{\text{\hspace{0.17em}and\hspace{0.17em}r}}_{\text{2}}$  in which a current i is flowing. The magnetic induction at the centre O will be   

 

 

 

     

The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards. 

$\therefore \text{B}={\text{B}}_{\text{1}}+{\text{B}}_{\text{2}}=\frac{{\mu }_{0}i}{4r_1}+\frac{{\mu }_{0}i}{4r_2}$

$=\frac{{\mu }_{0}i}{4r_1}\left(\frac{{\text{r}}_{\text{1}}+{\text{r}}_2}{{\text{r}}_{\text{1}}{\text{r}}_{\text{2}}}\right)\otimes$