Three positive charges of equal magnitude q are placed at the vertices of an equilateral triangle of side l. How can the system of charges be placed in equilibrium?

To keep the system in equilibrium, net force experienced by charges at  'A' ,'B' , and 'C' should be zero. For this, another charge of opposite signshould be placed at the centroid of the triangle. Let this charge be '-Q'.AD=lcos⁡30∘=l32,AO=23AD=l3For equilibrium of charge at C2F→CAcos⁡30∘=F→CO⇒2×14πε0×q2l2×32=14πε0Qq(l/3)2  ⇒Q=q3Thus, Q=-q3