Question

A circular loop and a square loop are formed from the same wire and the same current is passed through them. Find the ratio of their dipole moments

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

Answer 1

Answer: (B)

Suppose the length of wire is $l$.
When wire formed in circular loop then radius of loop
$r=\frac{l}{2\pi }$
Magnetic dipole $M_1=iA=i\pi r^2$
$=i\pi \times {\left(\frac{l}{2\pi }\right)}^2=i\times \frac{l^2}{4\pi }$
When wire formed in square loop then the side of loop
$a=l/4$
Magnetic dipole $M_2=IA=i\times a^2=i\times \frac{l^2}{16}$
$\therefore \frac{M_1}{M_2}=\frac{4}{\pi }$