Question

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 $2 a .$ The magnetic field due to this loop at the point $P(a, 0, a)$ points in the direction

• A. $\frac{1}{\sqrt{2}}(-\hat{j}+\hat{k})$
• B. $\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})$
• C. $\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$
• D. $\frac{1}{\sqrt{2}}(\hat{i}+\hat{k})$

Answer 1

Answer: (D)

Refer to figure, the direction of magnetic field at point $(a, 0, a)$ for the current due to portion $A B C D$ is pointing along $+z$ -axis i.e., represented by $\hat{k}$. The direction of magnetic field at the given point due to current in portion $D E F A$ is
pointing along $+x$ -axis i.e., represented by $i .$ Magnitude of magnetic field due to both the portions will be equal. Therefore, direction of resultant magnetic field at the given point will be $\frac{1}{\sqrt{2}}(\hat{i}+\hat{k})$