Q 12-04-109JEE MainJEE Main 2023 (30 Jan, Shift 2)Medium
As shown in the figure, a current of $2\ \text{A}$ flowing in an equilateral triangle of side $4\sqrt3\ \text{cm}$. The magnetic field at the centroid $O$ of the triangle is (Neglect the effect of earth's magnetic field)
Answer: (D) $3\sqrt3\times10^{-5}\ \text{T}$
Distance of the centroid from each side: $r=\dfrac{a}{2\sqrt3}=\dfrac{4\sqrt3}{2\sqrt3}=2\ \text{cm}$. Each side subtends $60^\circ$ on either side of the perpendicular:
$$B_1=\frac{\mu_0I}{4\pi r}(2\sin60^\circ)=10^{-7}\times\frac{2}{0.02}\times\sqrt3=\sqrt3\times10^{-5}\ \text{T}$$
All three sides add: $B=3\sqrt3\times10^{-5}\ \text{T}$.
Solution by Sreeraj P, M.Sc Physics