Two wires AO and OC carry equal currents I as shown in the figure where angle of AOC= ${60}^0.$ Find the magnitude of the magnetic field at the point P on the bisector of angle ${60}^0$ at a distance  r from O. Assume that the other ends of both wires extended to infinity

 

 

The Direction of magnetic field due to both the wires AO and OC are out of the page of  paper due to wire OC.

$B=\frac{{\mu }_{0}i}{4\pi d}[\sin {\varphi }_1+Sin{\varphi }_2]=\frac{{\mu }_{0}i}{4\pi d}[Sin(90-\theta /2)+\sin {90}^0] \because d=rSin\theta /2$

$B=\frac{{\mu }_{0}i}{4\pi rS\mathrm{in}\varphi /2}[1+\cos \varphi /2]$

Due to both the wires, the net magnetic field is $B=2\times \frac{{\mu }_{0}i}{4\pi rS\mathrm{in}\varphi /2}[1+\cos \varphi /2]$

$B=\frac{{\mu }_{0}i[1+\cos \varphi /2]}{2\pi rS\mathrm{in}\varphi /2}$