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/sqrt2(-hatj+hatk)`
B. `1/sqrt3(-hatj+hatk+hati)`
C. `1/sqrt3(hati+hatj+hatk)`
D. `1/sqrt2(hati+hatk)`

Answer

D

Explanation

the direction of magnetic field induction at a point (a, 0, a) for the current due to portion ABCD is pointing along z-axis i.e., represented by `hatk`. The direction of magnetic field induction at the given point due to current in portion DEFA is pointing +x axis i.e. represented by `hati`. Therefore, the effective direction of magnetic field induction is along the resultant of `hati` and `hatk` i.e., `1/sqrt2(hati+hatk)`