Question

A steel wire of length $L$ has a magnetic moment $M$. Then it is bent into a some circular arc subtending an angle ${180}^o$ at the centre, the new magnetic moment of the arc is :

• A. $M$
• B. $\frac{2M}{\pi }$
• C. $\frac{M}{L}$
• D. $ML$

Answer 1

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

Magnetic moment of a magnet = $ml$
where
$m=$ pole strength
$l=$ effective distance between the two poles
When it is bent to form a semicircle,
$\pi r=L$
$r=L/\pi$
Effective distance between the two poles $=2r$
$=2L/\pi$
$M_{initial}=mL$
$M_{final}=2mr$
$M_{final}=2mL/\pi$
$M_{final}=2M/\pi$