Q 12-04-013NEETNEET 2021Top questionMedium
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 :
Answer: (B) $\sqrt{3}Ia^2$ and $3Ia^2$
Magnetic moment: $m = NIA$.
(i) Triangle: perimeter $3a$, so $N = \dfrac{12a}{3a} = 4$ turns, each of area $\dfrac{\sqrt{3}}{4}a^2$:
$$m_1 = 4 \times I \times \frac{\sqrt{3}}{4}a^2 = \sqrt{3}Ia^2$$
(ii) Square: perimeter $4a$, so $N = 3$ turns, each of area $a^2$:
$$m_2 = 3Ia^2$$
Solution by Sreeraj P, M.Sc Physics