The location of three long wires carrying same current `I` are `x=-a`, `x=0` and `x=+` a respectively as shown in figure. The magnetic field at point (`0`, `0`, `a`) is

Options

A. `(mu_(0)I)/(2pia)`
B. `(mu_(0)I)/(sqrt(2)pia)`
C. `(mu_(0)I)/(2sqrt(2)pia)`
D. zero

Explanation

By symmetry, the net field is Zero
The net field at `P(0,0,a)`
`vecB=vecB_(A)+vecB_(0)+vecB_(c )`
`=(mu_(0)I)/(2piasqrt(2)){cos45^(@)hati+sin45^(@)(-hatk)}+(mu_(0)I)/(2pia)(-hati)+(mu_(0)I)/(2piasqrt(2)){cos45^(@)hati+sin45^(@)(hatk)}]`
`=(mu_(0)I)/(2piasqrt(2))sqrt(2)hati+(mu_(0)I)/(2pia)(-hati)`
`=(mu_(0)I)/(2pia)[hati-hati]=0`