A uniform conducting wire of length 24a and resistance R is wound up… | JEE Main 2021 (27 Aug, Shift 1)

Q57JEE Main 2021 · 27 AUG · SHIFT 1Medium

Current Loop as a Magnetic Dipole

A uniform conducting wire of length 24a and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1: $\sqrt{y}$ where y is ..................

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Same wire and same $V_0$ , so the same current $I$ in both cases. $M = NIA$ .
Triangle: $N = \frac{24a}{3a} = 8$ ; $M_t = 8I\cdot\frac{\sqrt{3}}{4}a^2 = 2\sqrt{3}Ia^2$ .
Square: $N = \frac{24a}{4a} = 6$ ; $M_s = 6Ia^2$ .
$\frac{M_t}{M_s} = \frac{2\sqrt{3}}{6} = \frac{1}{\sqrt{3}}$ , so $y = 3$ .

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