Tow wire AO and OC carry euqal current i. as shown in figure . One end of both the wire extends to infinity . Anlge AOC is `alpha` . The magnetiude of magnetic fields at a point P on the bisector of these two wirea at a distance r from point O is ltbgt

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))`