Question

A bar magnet of length $l$ and magnetic moment $M$ is bent to form a semicircle. The new dipole moment is

• A. $\frac{2M}{\pi }$
• B. $M$
• C. $\frac{\pi M}{2}$
• D. none of these

Answer 1

The correct option is A $\frac{2M}{\pi }$

Assume the poles of pole strength $m$ to be at the opposite ends of the magnet.
Dipole moment $M=m.l$
When the magnet is bent into semicircle, the new distance between the poles $l_{new}=2R$ where $\pi R=l$

$\therefore l_{new}=\frac{2l}{\pi }$

$M_{new}=m.l_{new}=m.\frac{2l}{\pi }=\frac{2M}{\pi }$