If a steel wire of length l and magnetic moment M is bent into a semicircular are, then the new magnetic moment is [JCECE 2012]

When wire is bent in the form of semicircular arc, then  $l=\pi r$

$\therefore$   The radius of semicircular arc,  $r=1/\pi$

Distance between two end points of semicircular wire

$=2r=\frac{2l}{\pi }$

$\therefore$  Magnetic moment of semicirculal, wire

$=m\times 2r=m\times \frac{2l}{\pi }=\frac{2}{\pi }ml$

But ml is the magnetic moment of wire, i.e. ml = M

$\therefore$  New magnetic moment  $=\frac{2}{\pi }M$