Question

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

• A. \( \frac{M}{\pi} \)
• B. \( \frac{2M}{\pi} \)
• C. \( \frac{3M}{\pi} \)
• D. \( \frac{4M}{\pi} \)

Hint:

When a wire is bent into a circular section, the magnetic moment depends on the angle subtended at the center of the circle.

Answer 1

The Correct Option is B

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) \( \frac{2M}{\pi} \).