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

Options

A. `(mu_0)/(2pi) i/r cot ((alpha)/2)`
B. `(mu_0)/(4pi) i/r cot ((alpha)/2)`
C. `(mu_0)/(2pi) i/r (1+cos(alpha)/2)/(sin(alpha/2))`
D. `(mu_0)/(4pi) i/r ((alpha)/2)`

Answer

C

Explanation

(c) `x=r sin(alpha)/2`

`:. B_P=2((mu_0)/(4pi))(i/x)[sin(90^@-(alpha)/2)+sin90^@]`
`=(mu_0)/(2pi) i/r ((1+cos(alpha)/2)/(sin(alpha)/2))`