Physics - Magnetism Question with Solution | TestHub

Let length of wire be $l$. For a square loop, side of square $\frac{l}{4}$. Hence its magnetic moment $M_{\mathrm{sq}}=iA=i{\left[\frac{l}{4}\right]}^2=\frac{i{l}^2}{16}$ Radius of a circular loop $r=\frac{l}{2\pi }$ Hence, its magnetic moment $\begin{array}{rl}& M_{\mathrm{cir}}=iA=i\pi r^2\\ & M_{\text{cir }}=i\pi \left[\frac{l^2}{4\pi r^2}\right]=\frac{i{l}^2}{4\pi }\\ & \Rightarrow \frac{M_{\text{cir }}}{M_{\mathrm{sq}}}=\frac{4}{\pi }\end{array}$