Question

A steel wire of length \( \ell \) has a magnetic moment \( M \). It is then bent into a semicircular arc. The new magnetic moment is:

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

Hint:

When a wire is bent into a semicircle, the magnetic moment doubles compared to a circular loop of the same radius.

Answer 1

The Correct Option is B

Step 1: The magnetic moment \( M \) of a current loop is given by \( M = I A \), where \( A \) is the area of the loop.
Step 2: When the wire is bent into a semicircular arc, the area is half of the area of a full circle with the same radius. Thus, the magnetic moment increases by a factor of 2. The new magnetic moment is \( \dfrac{2M}{\pi} \).

Final Answer: \[ \boxed{\dfrac{2M}{\pi}} \]