Two wires AO and OC carry equal currents i as shown in the figure where `angle AOC = theta` ,Find the magnitude of the magnetic field at the point P on the bisector of anlge `theta` at a distance 'r' from O. Assume that the other ends of both wires extend to infinity

Explanation

The direction of magnetic field due to both the wires AO and OC are out of page of paper
Due to wire OC
`B = (mu_0i)/(4pid){sin phi_1 + sin phi_2}`
`B = (mu_0i)/(4pisin""theta/2){sin (90 -theta/2) + sin 90}`
`B = (mu_0i)/(4pi sin ""theta/2)(1 + cos"" (theta)/(2))`
Due to both the wires, the net magnetic field is
`B = (2 xx mu_0i)/(4pir sin""theta/2)(1 + cos""theta/2)`
`B = (2 xx mu_0i)/(2pir sin""theta/2)(1 + cos""theta/2)`
`B = (mu_0)/(2pi) (i)/(r) cot ""(theta)/(4)`