A straight magnetic strip has a magnetic mome | vedclass

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Question

(A) Let the pole strength of the magnetic strip be $m$ and its length be $\ell$. The initial magnetic moment is $M_1 = m \ell = 44 	ext{ Am}^2$.When

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(A) Let the pole strength of the magnetic strip be $m$ and its length be $\ell$. The initial magnetic moment is $M_1 = m \ell = 44 	ext{ Am}^2$.When the strip is bent into a semicircle of radius $R$,the length of the strip becomes the arc length of the semicircle,so $\ell = \pi R$,which means $R = \frac{\ell}{\pi}$.The new magnetic moment $M_2$ is the product of the pole strength and the straight-line distance between the poles (the diameter of the semicircle),which is $2R$.$M_2 = m 	imes (2R) = m 	imes \left( \frac{2\ell}{\pi} ight) = \frac{2}{\pi} (m \ell)$.Substituting the given values: $M_2 = \frac{2}{\pi} 	imes 44 = \frac{2}{(22/7)} 	imes 44 = \frac{2 	imes 7}{22} 	imes 44 = \frac{14}{22} 	imes 44 = 14 	imes 2 = 28 	ext{ Am}^2$.

$A$ straight magnetic strip has a magnetic moment of $44 \text{ Am}^2$. If the strip is bent in a semicircular shape,its magnetic moment will be . . . . . . . $\text{Am}^2$ (Given $\pi = \frac{22}{7}$)

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