A wire carrying current I is bent in the shape ABCDEFA as shown… | JEE Main 2020 (2 Sep, Shift 2)

Q63JEE Main 2020 · 2 SEP · SHIFT 2Difficult

Current Loop as a Magnetic Dipole

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

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Answer: (c)

Split the wire into two loops ABCDA and ADEFA; the common side AD carries opposite currents and cancels.
ABCDA lies in the horizontal (XY) plane, area $ab$ : $\vec m_1 = abI\,\hat k$ .
ADEFA lies in the vertical (XZ) plane, area $ab$ : $\vec m_2 = abI\,\hat j$ .
$\vec m = abI(\hat j + \hat k)$ , magnitude $\sqrt2\,abI$ along $\frac{\hat j}{\sqrt2} + \frac{\hat k}{\sqrt2}$ .
So the answer is (c).

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Current Loop as a Magnetic Dipole question from JEE Main 2020 (2 Sep, Shift 2)

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