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Physics-

General

Easy

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

$\frac{1}{\sqrt{2}} (- \overset{}{\hat{j} + \hat{k}})$
$\frac{1}{\sqrt{3}} (- \hat{j} + \hat{k} + \hat{i})$
$\frac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$
$\frac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

The correct answer is: $fraction numerator 1 over denominator square root of 2 end fraction left parenthesis stack i with hat on top plus stack k with hat on top right parenthesis$

The magnetic field at $P left parenthesis a comma 0 comma a right parenthesis$ due to the loop is equal to the vector sum of the magnetic fields produced by loops ABCDA and AFEBA as shown in the figure.
Magnetic field due to loop ABCDA will be along $stack i with hat on top$ and due to loop AFEBA, along $stack k with hat on top$ . Magnitude of magnetic field due to both the loops will be equal.
Therefore, direction of resultant magnetic field at P will be $fraction numerator 1 over denominator square root of 2 end fraction left parenthesis stack i with hat on top plus stack k with hat on top right parenthesis$ .

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