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(A) Total length of wire $L = 12 a$.Case $(i)$: Equilateral triangle of side $a$.Perimeter of one turn $= 3 a$.Number of turns $N_{1} = \frac{12 a}{3

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$\sqrt{3} Ia^{2}$ and $3 Ia^{2}$

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(A) Total length of wire $L = 12 a$.Case $(i)$: Equilateral triangle of side $a$.Perimeter of one turn $= 3 a$.Number of turns $N_{1} = \frac{12 a}{3 a} = 4$.Area of one triangle $A_{1} = \frac{\sqrt{3}}{4} a^{2}$.Magnetic dipole moment $\mu_{1} = N_{1} I A_{1} = 4 	imes I 	imes \frac{\sqrt{3}}{4} a^{2} = \sqrt{3} I a^{2}$.Case $(ii)$: Square of side $a$.Perimeter of one turn $= 4 a$.Number of turns $N_{2} = \frac{12 a}{4 a} = 3$.Area of one square $A_{2} = a^{2}$.Magnetic dipole moment $\mu_{2} = N_{2} I A_{2} = 3 	imes I 	imes a^{2} = 3 I a^{2}$.Thus,the magnetic dipole moments are $\sqrt{3} I a^{2}$ and $3 I a^{2}$.

$A$ uniform conducting wire of length $12 a$ and resistance $R$ is wound up as a current-carrying coil in the shape of,
$(i)$ an equilateral triangle of side $a$.
$(ii)$ a square of side $a$.
The magnetic dipole moments of the coil in each case respectively are:

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$A$ uniform conducting wire of length $12 a$ and resistance $R$ is wound up as a current-carrying coil in the shape of,$(i)$ an equilateral triangle of side $a$.$(ii)$ a square of side $a$.The magnetic dipole moments of the coil in each case respectively are: