A wire of magnetic material of length 2L and | vedclass

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Question

(A) The original magnetic moment is $M = m(2L)$,where $m$ is the pole strength. When the wire is bent at the centre,it forms two segments of length $L

Vedclass · Accepted Answer

$\frac{M}{\sqrt{2}}$

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(A) The original magnetic moment is $M = m(2L)$,where $m$ is the pole strength. When the wire is bent at the centre,it forms two segments of length $L$,each having a magnetic moment $M' = m(L) = \frac{M}{2}$. These two segments are perpendicular to each other. The resultant magnetic moment $M_{net}$ is the vector sum of the two individual magnetic moments: $M_{net} = \sqrt{(\frac{M}{2})^2 + (\frac{M}{2})^2} = \sqrt{\frac{M^2}{4} + \frac{M^2}{4}} = \sqrt{\frac{2M^2}{4}} = \sqrt{\frac{M^2}{2}} = \frac{M}{\sqrt{2}}$.

$A$ wire of magnetic material of length $2L$ and magnetic moment $M$ is bent at the centre to form an $L$-shaped wire. Its magnetic moment is

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