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 $P (a, 0, a)$ point in the direction

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

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

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

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\frac{1}{\sqrt{2}} (^i +^j)

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Solution

The correct option is D $\frac{1}{\sqrt{2}} (^i +^j)$
The magnetic field at $P (a, 0, a)$ due to the loop is equal to the vector sum of the magnetic fields produced by loops $A B C D A$ and $A F E B A$ as shown in the figure.

Magnetic field due to loop $A B C D A$ will be along $^i$ and due to loop $A F E B A$ , along $^k$ . The magnitude of the magnetic field due to both the loops will be equal.

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

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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) point in the direction

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 $P (a, 0, a)$ point in the direction