Example : 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 charge Q (with the same sign as $q$) placed at the centroid of the triangle?

**Solution**In the given equilateral triangle ABC of sides of length $l$, if we draw a perpendicular AD to the side BC,

$AD=ACcos30=(3 /2)l$ and the distance AO of the centroid O from A is $(2/3)AD=(1/3 )l$. By symmetry AO = BO = CO.

Force $F_{1}$ on Q due to charge q at $A=4πϵ_{0}l_{2}3Qq $ along AO

Force $F_{2}$ on Q due to charge q at $B=4πϵ_{0}l_{2}3Qq $ along BO

Force $F_{3}$ on Q due to charge q at $C=4πϵ_{0}l_{2}3Qq $ along CO

Therefore, the total force on $Q=4πϵ_{0}l_{2}3Qq (r^−r^)=0$ where $r^$ is the unit vector along OA.