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Question

(D) Let the original length of the wire be $L$ and the pole strength be $m$. The original magnetic moment is $M = m 	imes L$.When the wire is bent in

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$(3M/\pi)$

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(D) Let the original length of the wire be $L$ and the pole strength be $m$. The original magnetic moment is $M = m 	imes L$.When the wire is bent into an arc of radius $r$ subtending an angle $	heta = 60^{\circ} = \pi/3$ radians at the center,the length of the arc is $L = r	heta = r(\pi/3)$.Thus,$r = 3L/\pi$.The new magnetic moment $M'$ is the product of pole strength $m$ and the straight-line distance (chord length) between the two ends of the arc.The chord length $d = 2r \sin(	heta/2)$.Substituting $	heta = 60^{\circ}$,we get $d = 2r \sin(30^{\circ}) = 2r(1/2) = r$.Substituting $r = 3L/\pi$,we get $d = 3L/\pi$.Therefore,$M' = m 	imes d = m 	imes (3L/\pi) = (3/\pi) 	imes (mL) = 3M/\pi$.

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