Question

An iron wire of length I is magnetized have a magnetic moment m. If it is bent inot a semicircle of radius r, its magnetic moment is

• A. m
• B. $\frac{2m}{\pi }$
• C. $\frac{m}{\pi }$
• D. $m\frac{1}{r}$

Answer 1

The correct option is B

$\frac{2m}{\pi }$

The magnetic moment of straight wire, $m=\left(q_m\right)\left(l\right)$
The magnetic moment of the semicircular wire, $m^{\prime }=\left(q_m\right)\left(2r\right)$
$\therefore \frac{m^{\prime }}{m}=\frac{2r}{l}=\frac{2r}{\pi r}=\frac{2}{\pi }\therefore m^{\prime }=\frac{2m}{\pi }$