A uniform conducting wire of length $12a$ and resistance '$R$' is wound up as a current carrying coil in the s

Question

A uniform conducting wire of length $12a$ 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

Accepted Answer

Current in the loop will be $I = V/R$ which is same for both loops. Magnetic moment of Triangle loop = $NIA$. $M_1 = (\frac{12a}{3a}) \cdot I \cdot \frac{\sqrt{3}}{4} a^2 = \sqrt{3}Ia^2$. Magnetic moment of square loop = $N'IA' = (\frac{12a}{4a}) \cdot I \cdot a^2 = 3Ia^2$.

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