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

Explanation

To keep the system in equilibrium, the net force experienced by charges at A, B and C should be zero. For this another charge of opposite sign should be placed at the centroid of the triangle. Let this charge be -Q.

`AD=l cos 30^(@)=(l sqrt(3))/2`
`AO=2/3 AD = (l)/(sqrt(3))=CO`
`2|vec F_(CA)| cos30^(@)=|vec F_(CO)|`
`|vec F_(CB)|=|vec F_(CA)|`
`2(1)/(4 pi epsilon) (q^(2))/(l^(2)) (sqrt(3))/(2)=(1)/(4 pi epsilon) (Qq)/(l//sqrt(3))` or `Q=q/(sqrt(3))`.