Three charged particles A,B and C with charges – 4q, 2q and -2q 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:

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$\frac{\sqrt{3} q}{π ε_{0} d^{2}}$

$\frac{3 \sqrt{3} q}{4 π ε_{0} d^{2}}$

$\frac{2 \sqrt{3} q}{π ε_{0} d^{2}}$

$\frac{\sqrt{3} q}{4 π ε_{0} d^{2}}$

answer is B.

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Detailed Solution

$\begin{array}{l} E l e c t r i c f i e l d d u e t o B a n d C i s a l o n g O C a n d \\ E l e c t r i c f i e l d d u e t o A i s a l o n g O A \\ A s p e r f i g u r e, t h e n e t h o r i z o n t a l c o m p o n e n t o f e l e c t r i c f i e l d i s \\ E_{n e t} = \frac{4 k q}{d^{2}} \times 2 \cos 30^{0} = \frac{q \sqrt{3}}{π ε_{0} d^{2}} \end{array}$

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