Discussion Forum



1)

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

Answer:

Option C

Explanation:

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

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

2352021484_p4.JPG

 Net intensity at point C is

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

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