Question

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

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

Answer 1

The correct option is C $\pi :4$

Suppose length of each wire is l.
$A_{square}={\left(\frac{l}{4}\right)}^2=\frac{l^2}{16}$
$A_{circle}=\pi r^2=\pi {\left(\frac{l}{2\pi }\right)}^2=\frac{l^2}{4\pi }$
$\because$ Magnetic moment
M=iA
$\Rightarrow \frac{M_{square}}{M_{circle}}=\frac{A_{square}}{A_{circle}}$
$\frac{l^2/16}{l^2/4\pi }=\frac{\pi }{4}$