Question

An iron wire of length $l$ is magnetized have a magnetic moment $m$. If it is bent into semicircle of radius $r$, its magnetic moment is.

• A. $m$
• B. $\frac{2m}{\pi }$
• C. $\frac{m}{\pi }$
• D. $m\frac{1}{r}$

Answer 1

Answer: (B)

$\frac{2m}{\pi }$

Given: Magnetic moment=m

Solution: As we know the formula of magnetic moment$M=polestrength\times l$ ....(1)

Where l is the distance between two poles

According to the question bar magnet is converted into semicircle which means that length is converted into the circumference but remember there is no change in the pole strength(m)

So, $l=\pi r$

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

$m^{{}^{\prime }}=polestrength\times 2r$ .......(2)

Where 2r= distance between two poles in semicircular form

Comparing eq (1) &(2) gives

$m^{{}^{\prime }}=\frac{2m}{\pi }$

Hence the correct answer is B