Physics | VITEEE 2015 | Discussion Page

Equal charges q each are placed at the vertices of an equilateral triangle of side r. The magnitude of electric field intensity at any vertex is

A) $\frac{2q}{4\pi\epsilon_{0}r^{2}}$

B) $\frac{q}{4\pi\epsilon_{0}r^{2}}$

C) $\frac{\sqrt{3}q}{4\pi\epsilon_{0}r^{2}}$

D) $\frac{\sqrt{2}q}{4\pi\epsilon_{0}r^{2}}$

Option C

Due to charge at A and B magnitude of intensity of electric field at point C

$E_{1}=E_{2}=\frac{1}{4\pi\epsilon_{0}}.\frac{q}{r^{2}}$

Net intensity at point C is

$E_{R}=\sqrt{E_{1}^{2}+E_{2}^{2}+2E_{1}E_{2}\cos 60^{0}}$

$E_{R}=\sqrt{E_{1}^{2}+E_{2}^{2}+2E_{1}^{2}\times\frac{1}{2}}=\sqrt{3}E_{1}=\frac{\sqrt{3}q}{4\pi \epsilon_{0}r^{2}}$

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