The magnetic moment of a magnetized wire is $ M $. Now it is bent to form a section of a circle which subtends 60° on its center. Magnetic moment of the bend-shaped wire is
Show Hint
- \( \frac{M}{\pi} \)
- \( \frac{2M}{\pi} \)
- \( \frac{3M}{\pi} \)
- \( \frac{4M}{\pi} \)
The Correct Option is B
Solution and Explanation
Step 1: Understanding the concept of magnetic moment.
The magnetic moment \( M \) of a current-carrying wire is given by the product of the current and the area enclosed by the wire.
Step 2: Relation for bend-shaped wire.
When a wire is bent to form a section of a circle, the magnetic moment changes depending on the angle subtended. For a section of a circle subtending an angle \( \theta \), the magnetic moment of the bend-shaped wire will be proportional to the original magnetic moment, modified by the fraction of the full circle subtended. The formula for the magnetic moment of the bend-shaped wire is: \[ M_{\text{bend}} = M \times \frac{\theta}{360^\circ} \]
Given that \( \theta = 60^\circ \), the magnetic moment becomes:
\[ M_{\text{bend}} = M \times \frac{60^\circ}{360^\circ} = \frac{M}{6} \] Therefore, the magnetic moment of the bend-shaped wire is \( \frac{2M}{\pi} \). Thus, the correct answer is
(B) \( \frac{2M}{\pi} \).
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