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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

A

`x=0`

B

`x=d/(sqrt(3))`

C

`x=-d/(sqrt(3))`

D

all

Text Solution

Verified by Experts

The correct Answer is:
D

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))`
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