Two wires AO and OC carry equal currents i as shown in figure. One end of both the wire extends to infinity. Angle AOC is $\alpha$. The magnitude of magnetic field at a point P on the bisector of these two wires at a distance r from point O is

• A

  $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{\mathrm{i}}{\mathrm{r}}\text{cot }\left(\frac{\alpha }{4}\right)$

• B

  $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{i}}{\mathrm{r}}\text{\hspace{0.17em}\hspace{0.17em}cot }\left(\frac{\alpha }{2}\right)$

• C

  $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{\mathrm{i}}{\mathrm{r}}\frac{\left(1+\cot \frac{\mathrm{\alpha }}{2}\right)}{\sin \left(\frac{\mathrm{\alpha }}{2}\right)}$

• D

  $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{i}}{\mathrm{r}}\left(\frac{\alpha }{2}\right)$