In vacuum, equal charges of the same nature are placed at the vertices of an equilateral triangle. What will be the electric field intensity and potential at the centroid of the triangle?

Explanation

Let three charges, each equal to +q, be placed at the vertices of the equilateral triangle. The length of the side of the triangle is r.
We know that the centroid of the triangle G divides the median of a triangle in the ratio 2:1.
Height of the equilateral triangle = `(sqrt3)/2 r`
So, potential at G is
`V = (q)/(4 pi epsilon_(0)(2/3 cdot (sqrt(3)r)/2)) xx 3 = (3q)/(4 pi epsilon_(0) cdot (r)/(sqrt3)) = (1)/(4 pi epsilon_(0))(3sqrt(3)q)/(r )`
If E be the electric field intensity at G due to each charge +q and if they are resolved into two perpendicular components, we see that the two components , `E cos 30^(@)` being equal and opposite balance each other. Again `2 E sin 30^(@) = (=(2E)/2 = E)` and E being equal and opposite, balance each other. So the electric field intensity at the centroid of the triangle is zero.