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))(-hat(j)+hat(k))`
B. `(1)/(sqrt(3))(-hat(j)+hat(k)+hat(i))`
C. `(1)/(sqrt(3))(hat(i)+hat(j)+hat(k))`
D. `(1)/(sqrt(2))(hat(i)+hat(k))`

Answer

D

Explanation

`(d)` Magnetic induction at `(a,0,a)` due to loop in `xy` plane is in `+k` direction. Due to loop in `yz` plane, the magnetic field will be in `(+hat(i))` direction. Due to both the loops, the direction of `vec(B)` will be `(1)/(sqrt(2))(hat(i)+hat(k))`