Question

A circular loop and a square loop are formed from two wires of same length and cross section. Same current is passed through them. Then, the ratio of their dipole moments is

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

Answer 1

Answer: (D)

Dipole moments due to current carrying circular
wire $M=i A$
Here, $ \frac{M_{1}}{M_{2}} =\frac{i \,\pi r^{2}}{i \,a^{2}}=\pi\left[\frac{\left(\frac{1}{2 \pi}\right)^{2}}{\left(\frac{1}{4}\right)^{2}}\right] $
$=\pi \frac{16}{4 \pi^{2}}=\frac{4}{\pi} $