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. $\frac{M}{\pi }$
• B. $\frac{2M}{\pi }$
• C. $\frac{3M}{\pi }$
• D. $\frac{4M}{\pi }$

Answer 1

Answer: (B)

Let, the pole strength of wire $=m$
Magnetic moment $=$ Pole strength $\times$ Separation between poles.
For straight wire:
Magnetic moment, $M=ml$
When a wire of length $l$ is bent in semi-circular shape, then, $l=\frac{\pi d}{2}$ .
where, $d$ is the diameter of a semi-circle.
$\Rightarrow d=\frac{2l}{\pi }$
Also in semi-circle, the separation between poles is its diameter.
Hence, the magnetic moment for semi-circle, $M^{{}^{\prime }}=m\left(\frac{2l}{\pi }\right)=\frac{2M}{\pi }$