Consider three charges `q_1,q_2,q_3` each equal to q at the vertices of an equilateral triangle of side l. what is the force on a charges Q ( with the same sign as q) placed at the centroid of the triangle,as shown in figure?

Explanation

The forces acting on charge q at a due to charges q at B and -q at c are `F_(12)` along BA and `F_(13)` along AC respectively q at a is given by
the force of attaraction or repulson for each pari of charges has the same magnitude `F=(q^(2))/(4piepsilon_(0)l^(2))`
The total force `f_(2)` on charge q at b is thus `f_(2)` =f `vecr_(2)` where `vecr_(2)` is a unit vector along AC
`F_(1)+F_(2)+F_(3)=0`
The result is not at all surprising it follows straight from the fact that colulomb law is consistent with newton thrid law the proof is left to you as an exercise