Consider three charged spheres made of some insulating material . Two of them are positively charged with charge Q and one is negatively charged with charged -q. What should be the charge ratio so that the three of them remain in equilibrium ? Assume the sizes to be very small .

Explanation

Charge distribution on spheres is assumed to be uniform and in such a case sphere behaves like point charge kept at its centre . The middle negative charge is being attracted by both identical positive charges so it will remain in equilibrium anyway. Equilibrium of positive charges requires that their repulsion is balanced by attraction of the middle negative charge.
`F_1=(qQ)/(4piepsilon_0 (r_1+r_2)^2)`
`F_2=Q^2/(4piepsilon_0 [2(r_1+r_2)]^2)`
For equilibrium we require `F_1 =F_2` , and on solving we get Q/q=4 .