Question

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

​​​​​​​$[$1 Mark$]$

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

Answer 1

The correct option is B $\frac{2M}{\pi }$

Magnetic moment of a wire of length $l$ is
$M=ml$


where $m$ is the strength of each pole.
When the wire is bent into a semicircle of radius $r$, then

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


Now, the distance between two poles

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

Its new magnetic moment is

$M^{\prime }=m\times 2r=m\times \frac{2l}{\pi }=\frac{2}{\pi }(m\times l)=\frac{2M}{\pi }$