Question

If three particles of each charge \( +q \) are placed at the three vertices of an equilateral triangle of side \( \sqrt{3}r \), then the net electric field at the centroid of the triangle is:

• A. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{q}{r} \)
• B. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{q}{r^2} \)
• C. \( \frac{1}{4\pi\varepsilon_0} \cdot \frac{3q}{r^2} \)
• D. zero

Hint:

In symmetric charge configurations (like an equilateral triangle), equal charges produce a net electric field of zero at the centroid.

Answer 1

The Correct Option is D

In an equilateral triangle, the centroid is equidistant from all vertices. Since all three charges are equal and positive, the electric field vectors at the centroid due to each charge are equal in magnitude and symmetrically placed at \(120^\circ\) to one another. 
Due to this symmetry, the vector sum of the electric fields cancels out. 

Thus, the net electric field at the centroid is zero.