A wire of length 8 m is bent to form a circular loop in y-z plane. A current of 0.5 A is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is: (a) -8i A m² (b) 8/ A m² (c) -4 A m² (d) 4 A m²

Answer: (b). 2π r = 8 ⇒ r = 4/π m, so A = π r² = 16/π m ². |M| = IA = 0.5×16/π = 8/π A m ². Loop in the y-z plane with anticlockwise current (seen from +x): by the right-hand rule M is along +i. So the answer is (b) 8/ A m ².

A wire of length 8 m is bent to form a circular loop in y-z plane. A… | JEE Main 2022 (30 Jul, Shift 2)

Q46JEE Main 2022 · 30 JUL · SHIFT 2Medium

Current Loop as a Magnetic Dipole

A wire of length $8\text{ m}$ is bent to form a circular loop in y-z plane. A current of $0.5\text{ A}$ is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is:

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Answer: (b)

$2\pi r = 8 \Rightarrow r = \frac{4}{\pi}$ m, so $A = \pi r^2 = \frac{16}{\pi}$ m $^2$ .
$|M| = IA = 0.5\times\frac{16}{\pi} = \frac{8}{\pi}$ A m $^2$ .
Loop in the y-z plane with anticlockwise current (seen from $+x$ ): by the right-hand rule $\vec{M}$ is along $+\hat{i}$ .
So the answer is (b) $\frac{8}{\pi}\hat{i}$ A m $^2$ .

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