Three long wires, each carrying current `i` are placed as shown. The middle wire is along `Y`-axis. The locus of point on the `X`-axis where magnetic field is zero is

Options

A. `x=0`
B. `x=d/(sqrt(3))`
C. `x=-d/(sqrt(3))`
D. all

Answer

D

Explanation

Due to wires `(1)` and `(2)`, magnetic field is zero on the middle wire i.e. `x=0`
`B_(1)=(mu_(0)i)/(2pi(d+x)), ox, B_(2)=(mu_(0)i)/(2pix), ox, B_(3)=(mu_(0)i)/(2pi(d-x)), o.`
`B_(P)=0 implies B_(1)+B_(2)=B_(3)implies 1/(d+x)+1/x=1/(d-x)`
`x=+-d/(sqrt(3))`