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 $M_{1}=i A=i \pi r^{2}$
$=i \pi \times\left(\frac{l}{2 \pi}\right)^{2}=i \times \frac{l^{2}}{4 \pi}$
When wire formed in square loop then the side of loop
$a=l / 4$
Magnetic dipole $M_{2}=I A=i \times a^{2}=i \times \frac{l^{2}}{16}$
$\therefore \frac{M_{1}}{M_{2}}=\frac{4}{\pi}$