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))/(2pir) i/r cot((alpha)/2)`
B. `(mu_(0))/(4pir) 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

`x=rsin((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)))`