Three charged particles $A, B$ and $C$ with charges $-4 q, 2 q$ and $-2 q$ are present on the circumference of a circle of radius $d$. The charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in figure. Electric field at $O$ along $x$-direction is:
Correct Option: 1
(1)
Electric field due to charge $+2 q$ at centre $O$
$\vec{E}_{1}=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{2 q}{d^{2}}\left[\frac{\sqrt{3} \hat{i}-\hat{j}}{2}\right]$
Electric field due to charge $-2 q$ at centre $O$
$\vec{E}_{2}=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{2 q}{d^{2}}\left[\frac{\sqrt{3} \hat{i}-\hat{j}}{2}\right]$
Electric field due to charge $-4 q$ at centre $O$
$\vec{E}_{3}=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{4 q}{d^{2}}\left[\frac{\sqrt{3} \hat{i}+\hat{j}}{2}\right]$
$\therefore$ Net electric field at point $O$
$\vec{E}_{0}=\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}=\frac{\sqrt{3} q}{\pi \varepsilon_{0} d^{2}} \hat{i}$
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