Question

Three point charges q, 2q and 8q are to be placed on a 9 cm long straight line. Find the position where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the position of the charge q due to the other two charges ? 

Answer 1

As potential energy of two point charges separated by a distance r is given by U(=q₁q₂/4πε₀r), so to have minimum potential energy the charges of greater value should be farthest, i.e., q must be between 2q and 8q. Let q be at a distance x from 2q, then potential energy of the system will be

i.e., 2x = (d – x) or x = (d/3) = (9/3) = 3 cm

So to have minimum potential energy, the charge q must be placed at a distance of 3 cm from 2q between 2q and 8q on the line joining the charges. In this situation, Field at q