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)

$\frac{4}{\pi }$

Answer 2

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 $M_{2}=I A=i \times a^{2}=i \times \frac{l^{2}}{16}$ $\therefore \frac{M_{1}}{M_{2}}=\frac{4}{\pi}$