A bar magnet of length l and magnetic dipole | vedclass

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(B) Let $m$ be the pole strength of each pole of the bar magnet of length $l$. Then,the initial magnetic dipole moment is given by:$M = m 	imes l$ ..

Vedclass · Accepted Answer

$\frac{3}{\pi} M$

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(B) Let $m$ be the pole strength of each pole of the bar magnet of length $l$. Then,the initial magnetic dipole moment is given by:$M = m 	imes l$ ......... $(i)$When the bar magnet is bent into an arc of radius $r$ subtending an angle $	heta = 60^{\circ} = \frac{\pi}{3} 	ext{ radians}$ at the center,the arc length $l$ is:$l = r 	heta = r 	imes \frac{\pi}{3}$$r = \frac{3l}{\pi}$The new magnetic dipole moment $M^{\prime}$ is the product of pole strength $m$ and the straight-line distance (chord length) between the two poles.The chord length $d$ is given by $2r \sin(\frac{	heta}{2}) = 2r \sin(30^{\circ}) = 2r 	imes \frac{1}{2} = r$.Thus,$M^{\prime} = m 	imes d = m 	imes r$.Substituting $r = \frac{3l}{\pi}$:$M^{\prime} = m 	imes \frac{3l}{\pi} = \frac{3}{\pi} (m 	imes l) = \frac{3}{\pi} M$ (using equation $(i)$).

$A$ bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be

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