Three charges +q, -q and +q are kept at the corners of an equilateral triangle of side d. Find the resultant electric force on a charge +q 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)/(sqrt3)`

In magnitude `F_(1) = F_(2) = F_(3) = (1)/(4pi in_(0)) (3q^(2))/(d^(2))`
Resultant of `F_(1) and F_(2) " is " F_(4) = (1)/(4pi in_(0)) (3q^(2))/(d^(2))` (an 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) = (3q^(2))/(2pi in_(0)d^(2))`