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

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$\frac{1}{\sqrt{2}} (- \hat{j} + \hat{k})$

$\frac{1}{\sqrt{3}} (- \hat{j} + \hat{k} + \hat{i})$

$\frac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$

$\frac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

answer is D.

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Detailed Solution

We can consider the non- planar loop as made by two loops ABCDA and AQRBA as shown in figure
Question Image

Magnetic field due to loop ABCDA will be along x-axis and due to loop AQRBA along z-axis, magnitude of magnetic field due to both loops will be equal
Question Image

Therefore, direction of resultant magnetic field at P will be along $\frac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

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