Three charged particles A , B and C with charges - 4 q , 2 q and - 2 q are present on the circumference of a…

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

1. $\frac{\sqrt{3}q}{\pi {\epsilon }_0{d}^2}$
2. $\frac{2\sqrt{3}q}{\pi {\epsilon }_0{d}^2}$
3. $\frac{\sqrt{3}q}{4\pi {\epsilon }_0{d}^2}$
4. $\frac{3\sqrt{3}q}{4\pi {\epsilon }_0{d}^2}$

Solution

$E_{net}=\frac{4kq}{d^2}\times 2\mathrm{c}\mathrm{o}\mathrm{s}30°=\frac{q\sqrt{3}}{\pi {\epsilon }_0{d}^2}$

Asked in: JEE Main 2020 (08 Jan Shift 1)

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