A long wire carrying `i` is bent to form a plane angle `theta`.Find the magnetic field `B` at a point on the bisector of this angle situated at a distance `x` from the vertex is written in the form of `K cot theta/4`Tesla.Then, find the value of `K`.

Options

A. `(mu_(0)i)/(pid)cot ((theta)/4), o.`
B. `(mu_(0)i)/(2pid)cot ((theta)/4), o.`
C. `(mu_(0)i)/(4pid)cot ((theta)/2), o.`
D. `(mu_(0)i)/(4pid)cot ((theta)/4), o.`

Answer

B

Explanation

`B_(1)=(mu_(0)i)/(4pidsin (theta/2)[cos (theta/2)+cos0]`
`=(mu_(0)i)/(4pid{2sin (theta/4)cos(theta/4}){2cos^(2)(theta/4)-1+1}`
`=(mu_(0)i)/(4pid)cos(theta/4)=B_(2), o.`
`B_(O)=B_(1)+B_(2)=(mu_(0)i cot((theta)/4))/(2pid), o.`