Three chargers +q, -q and + q are kept at the corners of an equilateral triangle of side d. Find the resultant electric force on a charge to placed at the centroid O of the triangle.

Explanation

Let the force acting on +q charge at O due to +q at A be `F_1, +q` at B be `F_2` and `-q` at C be `F_3`
Here `AO = OB = OC = d/(sqrt(3))`

In magnitude `F_1 = F_2 = F_3 = 1/(4 pi epsilon_0) (3q^2)/(d^2)`
Resultant of `F_1` and `F_2` is `F_4 = 1/(4 pi epsilon_0) (3q^2)/(d^2)`
(as angle between `F_1 and F_2` is `120^@`)
Direction of `F_4` is along the direction of `F_3`. Hence the resultant force on +q at O is
`F = F_3 + F_4 = (3 q^2)/(2 pi epsilon_0 d^2)` .