Consider the charges q.q and -q placed at the vertices of an equilateral triangles as .Show in figure. What is the force on each charges?
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Explanation

The forces acting on charges q at A due to charges q at B and -q at C are `F_(12) ` along BA and `F_(12) ` along AC respectively as shown in figure. By the parallelogram law. The total force ` F_1 ` on the charges q at A is given by `F_1 = F hatr_(1) " where " hatr _1 ` is a unit vector along BC.
The force of atraction or repulsion for each pair of charges has the same magnitude ` F-(q^(2))/( 4pi in _0l^(2))`
The total force ` F_2` on charges q at B is thus `F_2 =F hat r _2.` where hat `r_2` is a unit vector along AC
Similarly the total force on charge -at C is ` F_3= sqrt 3 hatn " where "hat n` is the unit vector along the direction bisecting the `angle BCA ` The sum of the forces on the three charges is zero, i.e.
` F_1+F_2+F_3=0 ` (for the system)
The result follows straight from the fact that Coulomb.s law is consistant with Newton.s third law.