Question

Two wires of same length are shaped into square and a circle. if they carry same current ratio of magnetic moment is

• A. $2:\pi$
• B. $\pi :3$
• C. $\pi :4$
• D. $1:\pi$

Answer 1

Answer: (C)

$\pi :4$

Let length of wire be $l$. For a square loop, side of square $\frac{l}{4}$.

Hence its magnetic moment
$M_{sq}=iA=i{\left[\frac{l}{4}\right]}^2=\frac{i{l}^2}{16}$
Radius of a circular loop $r=\frac{l}{2\pi }$.

Hence, its magnetic moment
$M_{cir}=iA=i\pi r^2$
$M_{cir}=i\pi \left[\frac{l^2}{4{\pi }^2}\right]=\frac{i{l}^2}{4\pi }$
$\Rightarrow \frac{M_{sq}}{M_{cir}}=\frac{\pi }{4}$