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(D) Let $m$ be the pole strength of the magnetized rod.The magnetic moment of the straight rod is given by $M = m L$.When the rod is bent into a semic

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

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(D) Let $m$ be the pole strength of the magnetized rod.The magnetic moment of the straight rod is given by $M = m L$.When the rod is bent into a semicircular arc of radius $R$,the length of the arc is equal to the original length of the rod:$L = \pi R \implies R = \frac{L}{\pi}$.The magnetic moment of the semicircular arc is the product of the pole strength and the straight-line distance between the two poles (the diameter of the semicircle):$M_{arc} = m(2R)$.Substituting the value of $R$:$M_{arc} = m \left( 2 \cdot \frac{L}{\pi} \right) = \frac{2}{\pi} (m L)$.Since $M = mL$,we get:$M_{arc} = \frac{2 M}{\pi}$.

$A$ thin rod of length $L$ is magnetized and has a magnetic moment $M$. The rod is then bent into a semicircular arc. The magnetic moment in the new shape is

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