Physics - Magnetism Question with Solution | TestHub

Length of the wire $L=12a$.

For the equilateral triangular coil of side $a$:
Perimeter of one turn $=3a$
Number of turns $N_t=\frac{12a}{3a}=4$
Area of the triangular coil $A_t=\frac{\sqrt{3}}{4}{a}^2$
Magnetic dipole moment $M_t=N_{t}I{A}_t=4\times I\times \frac{\sqrt{3}}{4}{a}^2=\sqrt{3}I{a}^2$

For the square coil of side $a$:
Perimeter of one turn $=4a$
Number of turns $N_s=\frac{12a}{4a}=3$
Area of the square coil $A_s=a^2$
Magnetic dipole moment $M_s=N_{s}I{A}_s=3\times I\times a^2=3I{a}^2$

Ratio of magnetic dipole moments:
$\frac{M_t}{M_s}=\frac{\sqrt{3}I{a}^2}{3I{a}^2}=\frac{1}{\sqrt{3}}$

Answer: $1:\sqrt{3}$