Magnetic Properties of Matter: Practice Problem & Solution
A uniform conducting wire of length $12\text{ a}$ 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: (2021)
Solution Explained:
To solve this problem, we apply the core principles of Magnetic Properties of Matter. Understanding the underlying formula is key to arriving at the correct answer below:
For triangle, $N_1 = 4$, $A_1 = \frac{\sqrt{3}}{4}a^2$, so $M_1 = \sqrt{3}Ia^2$. For square, $N_2 = 3$, $A_2 = a^2$, so $M_2 = 3Ia^2$.
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