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

Dipole moment $M=IA$, where $I=$current flowing through the wire of loop and $A$= area 

Let length of the wire be L.

 $\therefore 2\mathrm{\pi R}=\mathrm{L}$ & for square $l=L/4$

$\therefore \frac{M_c}{M_s}=\frac{{\mathrm{I\pi R}}^2}{\mathrm{I} l^2}=\frac{\mathrm{\pi }{\displaystyle \frac{{\mathrm{L}}^2}{4{\mathrm{\pi }}^2}}}{{\displaystyle \frac{L^2}{16}}}$

$\Rightarrow \frac{M_c}{M_s}=\frac{{\mathrm{\pi L}}^2}{4{\mathrm{\pi }}^2}\times \frac{16}{L^2}=\frac{4}{\mathrm{\pi }}$

$\Rightarrow \frac{M_s}{M_c}=\frac{\mathrm{\pi }}{4}$