A regular hexagone of side a. A wire of length 24 a is coiled on...

Let number of turns $=\mathrm{n}$ $$\begin{aligned} & n \times 6 a=24 a \\ & \therefore \quad n=4 \\ & \end{aligned}$$ Magnetic moment, $\mathrm{M}=\mathrm{nIA}=$ 4IA $$\begin{aligned} & \because \text{ Area\text{ of } hexagone }=\frac{1}{2} \mathrm{a}^2 \sin 60^{\circ}+\mathrm{a} \cdot 2 \mathrm{a} \sin 60^{\circ} \\ & \quad+\frac{1}{2} \mathrm{a}^2 \sin 120^{\circ}\end{aligned}$$=\frac{\sqrt{3}}{4} a^2+\sqrt{3} a^2+\frac{\sqrt{3} a^2}{4}=\frac{6 \sqrt{3} a^2}{4}=\frac{3 \sqrt{3} a^2}{2}$Hence, magnetic moment$=4 I\left(\frac{3 \sqrt{3} a^2}{2}\right)=6 \sqrt{3} a^2$