A magnetized wire of magnetic moment M and le | vedclass

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Question

(A) The initial magnetic moment is $M = m \cdot l$,where $m$ is the pole strength.When the wire of length $l$ is bent into a semicircle,the length $l$

Vedclass · Accepted Answer

$\frac{2 M}{\pi}$

Vedclass · Answer

(A) The initial magnetic moment is $M = m \cdot l$,where $m$ is the pole strength.When the wire of length $l$ is bent into a semicircle,the length $l$ becomes the arc length of the semicircle.So,$l = \pi r$,which gives $r = \frac{l}{\pi}$.The new distance between the poles (the diameter of the semicircle) is $l' = 2r = \frac{2l}{\pi}$.The new magnetic moment $M'$ is given by the product of the pole strength and the new distance between the poles:$M' = m \cdot l' = m \cdot \left(\frac{2l}{\pi}\right) = \frac{2}{\pi} (m \cdot l)$.Since $M = m \cdot l$,we have $M' = \frac{2M}{\pi}$.

$A$ magnetized wire of magnetic moment $M$ and length $l$ is bent into the form of a semicircle of radius $r$. Then its new magnetic moment is:

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