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Q.

A wire carrying 3A current is wrapped around a non-conducting cube of side 1m as shown below. Find the magnitude of net magnetic moment M due to the loop (in S.I. unit). Find 2M = ?

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answer is 9.

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Detailed Solution

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Here $\vec{M} = - i a^{2} \hat{i} - i \frac{a^{2}}{2} \hat{j} - i a^{2} \hat{k}$

$\vec{M} = - i a^{2} (\hat{i} + \frac{\hat{j}}{2} + \hat{k}) \Rightarrow | \vec{M} | = \frac{3}{2} i a^{2}$

$= \frac{3}{2} \times 3 \times 1 | \vec{M} | = \frac{9}{2}$ amphere - ${meter}^{2}$

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