Two point charges `q_(1)`, and `q_(2)` are kept at a distance of `r_(12)` in air. Deduce the expression for the electrostatic potential energy of this system.

Explanation

Let a point charge 4, be situated at a given point A. Electric potential due to it at another point B, situated at a distance `r_(12)` will be
`V= (1)/(4pi in_(0)).(q_(1))/(r_(12))`
If a point charge `q_(2)` is brought from infinity to point B, then work done to bring this charge against the field of charge `q_(1)` will be
`W= q_(2)V= (1)/(4pi in_(0)). (q_(1)q_(2))/(r_(12))`
This work done is stored in the system of two point charges as their electrostatic potential energy U. Thus
`U= (1)/(4piin_(0)).(q_(1)q_(2))/(r_(12))`