A non - popular loop of conducting wire carrying a current `I` is placed as shown in the figure . Each of the straighrt sections of the loop is of the length ` 2a`. The magnetic field due to this loop at the point `P(a, 0 ,a)` points in the direction

Options

A. `1/(sqrt(2))(-hatj+hatk)`
B. `1/(sqrt(3))(-hatj+hatk+hati)`
C. `1/(sqrt(3))(hatj+hatk+hati)`
D. `1/(sqrt(2)(hati+hatk)`

Answer

D

Explanation

By placing two wires each of length `2a`, along `y`-axis, complete the square loop in `y-z` plane and in `x-y` plane.
From `P(a,0,a):`
Current in loop `①` is anticlockwise, hence magnetic field at `P` will be towards observer i.e.
`vec(B)_(1)=Bhati`
Current in loop `②` anti clockwise,
`vec(B)_(2)=B hatk`
`vec(B)_(P)=vec(B)_(1)+vec(B)_(2)=B hati+Bhatk`
`hat(B)_(P)=(vec(B)_(P))/(|vec(B)_(P)|)=(Bhati+Bhatk)/(sqrt(2)B)=1/(sqrt(2))(hati+hatk)`