Question

A steel wire of length $l$ has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

• A. $M$
• B. $2M/\pi$
• C. $M/l$
• D. $M\times l$

Answer 1

Answer: (B)

When wire is bent, length $l=\pi r$, where $r$ is the radius of the semicircular are , $\therefore$ $r=l/\pi$
Distance between two poles of semicircular wire = $2r=2l/pi$
Magnetic moment of semicircular wire = $m\times 2r=m\times 2l/\pi =\frac{2}{\pi }ml$
But $ml$ is the magnetic moment of straight wire $i.e.ml$ = M
$\therefore$ New magenetic moment of straight wire $i.e.ml$ = M
$\therefore$ New magnetic moment = 2M/$\pi$