Question 112 of 311

Three charged particles $\text{A}, \text{B}$ and $\text{C}$ with charges $-4q,2q$ and $-2q$ are present on the circumference of a circle of radius $d.$ The charged particles $\text{A}, \text{C}$ and centre $\text{O}$ of the circle formed an equilateral triangle as shown in the figure. The electric field at the point $\text{O}$ is

A$\dfrac{\sqrt{3}q}{\pi {\epsilon }_{0}{d}^{2}}$B$\dfrac{2\sqrt{3}q}{\pi {\epsilon }_{0}{d}^{2}}$C$\dfrac{\sqrt{3}q}{4\pi {\epsilon }_{0}{d}^{2}}$D$\dfrac{3\sqrt{3}q}{4\pi {\epsilon }_{0}{d}^{2}}$

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Answer: (A) $\dfrac{\sqrt{3}q}{\pi {\epsilon }_{0}{d}^{2}}$

${E}_{net}=\dfrac{4kq}{{d}^{2}}\times 2cos30^{\circ}=\dfrac{q\sqrt{3}}{\pi {\epsilon }_{0}{d}^{2}}$