Two wires of equal lengths are shaped in the form of a square loop and a circular loop. Both loops are suspended in a uniform magnetic field. Prove that for the same current, the circular loop will experience larger torque.

Let the length of the wire be \(\displaystyle l\). For square loop; \(\displaystyle l=4 a \Rightarrow a=\frac{l}{4}\) Area of square loop \(\displaystyle =a^{2}=\frac{l^{2}}{16}\) For Circular loop; \(\displaystyle l=2 \pi r \Rightarrow r=\frac{l}{2 \pi}\) Area of circular \(\displaystyle \operatorname{loop}\left(\mathrm{A}_{\mathrm{c}}\right)=\pi r^{2}=\frac{l^{2}}{4 \pi}\) Torque acting on the loop \(\displaystyle (\tau) \alpha \mathrm{A}\) \[\because \mathrm{A}_{\mathrm{c}}>\mathrm{A}_{s} \quad \therefore \tau_{\mathrm{c}}>\tau_{s} \] &