Question

If a steel wire of length $l$ and magnetic moment $M$ is bent into semicircular arc, then the new magnetic moment is

• A. $M\times l$
• B. $\frac{M}{l}$
• C. $\frac{2M}{\pi }$
• D. $M$

Answer 1

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

When wire is bent in the form of semicircular arc then, $l=\pi r$
$\therefore$ The radius of semicircular arc, $r=l/\pi$
Distance between two end points of semicircular wire $=2r=\frac{2l}{\pi }$
$\therefore$ Magnetic moment of semicircular wire
$=m\times 2r=m\times \frac{2l}{\pi }=\frac{2}{\pi }ml$
But $ml$ is the magnetic moment of straight wire
i.e., $ml=M$
$\therefore$ New magnetic moment $=\frac{2}{\pi }M$