Three magnets of the same length but moments M, $2$ M and $3$ M are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant magnetic moment of the arrangement is?

6

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Zero

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\sqrt{3}

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\frac{\sqrt{3}}{2}

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Solution

The correct option is C $\sqrt{3}$ M
$\to M = (M - 2 M cos 60 - 3 M cos 60)^i + (2 M cos 30 - 3 M cos 30)$
$\to M = \frac{- 3}{2} M^i - \frac{\sqrt{3}}{2} M$
$M = | \to M | = \sqrt{{(\frac{3}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}} M = \sqrt{3} M$
Magnetic moment $= \sqrt{3} M$

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Three magnets of the same length but moments M, 2M and 3M are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant magnetic moment of the arrangement is?

The correct option is C √3M→M=(M−2Mcos60−3Mcos60)^i+(2Mcos30−3Mcos30)→M=−32M^i−√32MM=|→M|= ⎷(32)2+(√32)2M=√3MMagnetic moment =√3M

Three magnets of the same length but moments M, $2$ M and $3$ M are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant magnetic moment of the arrangement is?

The correct option is C $\sqrt{3}$ M
$\to M = (M - 2 M cos 60 - 3 M cos 60)^i + (2 M cos 30 - 3 M cos 30)$
$\to M = \frac{- 3}{2} M^i - \frac{\sqrt{3}}{2} M$
$M = | \to M | = \sqrt{{(\frac{3}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}} M = \sqrt{3} M$
Magnetic moment $= \sqrt{3} M$