Three charged particles A, B and C with charges –4q, 2q and –2q are… | JEE Main 2020 (8 Jan, Shift 1)

Q37JEE Main 2020 · 8 JAN · SHIFT 1Medium

Electric Field & Field Lines

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 form an equilateral triangle as shown in figure. Electric field at O along x-direction is:

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Answer: (c)

Let $E_0 = \dfrac{q}{4\pi\varepsilon_0 d^2}$ . A ( $-4q$ ) at $30^\circ$ , C ( $-2q$ ) at $-30^\circ$ , and B ( $2q$ ) is on line $CO$ extended (at $150^\circ$ ).
A: field towards A, $x$ -component $4E_0\cos 30^\circ = 2\sqrt{3}E_0$
C: field towards C, $x$ -component $2E_0\cos 30^\circ = \sqrt{3}E_0$
B: field away from B (towards C), $x$ -component $2E_0\cos 30^\circ = \sqrt{3}E_0$
$E_x = 4\sqrt{3}E_0 = \dfrac{\sqrt{3}q}{\pi\varepsilon_0 d^2}$
So the answer is (c).

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