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)

$2M/\pi$

Answer 2

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/$\pi$