Step 1: Understanding the Concept:
Magnetic moment (\(M\)) of a bar magnet is the product of its pole strength (\(m\)) and the effective length (\(L\)) between the poles.
When a bar magnet is bent, its pole strength remains unchanged, but the effective distance (the straight-line distance between the poles) changes.
The new magnetic moment is \(M' = m \times l\), where \(l\) is the chord length.
Step 2: Key Formula or Approach:
Initial moment: \(M = m \cdot L\).
Length of arc: \(L = R \theta\) (where \(\theta\) is in radians).
Chord length (effective length): \(l = 2R \sin(\theta/2)\).
Step 3: Detailed Explanation:
The angle is \(\theta = 60^\circ = \frac{\pi}{3}\) radians.
Step 1: Relate the original length \(L\) to the radius \(R\) of the arc.
\[L = R\theta = R \left(\frac{\pi}{3}\right) \implies R = \frac{3L}{\pi}\]
Step 2: Find the new effective distance \(l\) between the ends of the bent bar.
\[l = 2R \sin\left(\frac{60^\circ}{2}\right) = 2R \sin 30^\circ\]
\[l = 2R \times \frac{1}{2} = R\]
Step 3: Calculate the new magnetic moment \(M'\).
\[M' = m \cdot l = m \cdot R\]
Substitute the value of \(R\) from Step 1:
\[M' = m \cdot \left(\frac{3L}{\pi}\right)\]
Since the original magnetic moment is \(M = m \cdot L\):
\[M' = \frac{3M}{\pi}\]
This corresponds to option (A).
Step 4: Final Answer:
The new magnetic moment is reduced by the ratio of the chord length to the arc length, resulting in \(3M/\pi\).