Consider three charges q₁, q₂, q₃ each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle?

Suppose the given charges are placed as shown in figure

Given that the triangle is equilateral so if O is the centroid of the triangle then,

AO = BO = CO = r

Force on charge Q due to q_1,

Force on charge Q due to q_2,

Force on charge Q due to q_3,

By the principle of superposition, total force on the charge Q is,

Since q₁ = q₂ = q₃

Since the triangle is equilateral hence angle between all the sides is 60^o

So the angle between is 120^o

So they form a triangle of cyclic vectors. Consequently,

Hence

The total force on charge q is zero