Question

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. \( \frac{\sqrt{2}q}{4\pi\epsilon_0 r^2} \)

Hint:

The electric field at the vertex of an equilateral triangle formed by charges is the result of the vector sum of the fields from the other two charges.

Answer 1

The Correct Option is C

For an equilateral triangle with charges at the vertices, the resultant electric field at any vertex is the vector sum of the electric fields due to the other two charges. This results in a field of magnitude \( \frac{\sqrt{3}q}{4\pi\epsilon_0 r^2} \).