Question

A straight steel wire of length $L$ has a magnetic moment $M$. When it is bent in the form of a semi-circle its magnetic moment will be

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

Answer 1

Answer: (C)

$\frac{2M}{\pi }$

Initial magnetic moment $M=ml$
when it is bent in a semi circular wire the effective length between the poles become $2R$
where $\pi R=l$
$R=l/\pi$

Therefore, new $M_{new}=m{l}_{eff}=m\times 2\times R=\frac{m\times 2\times l}{\pi }=\frac{2M}{\pi }$