Derivation of electric potential energy of a system of two point charges in the absence of external electric field

We have to consider two charges q_{​1 ,} q_2​, located at r₁ and r_​2 respectively. The work done in bringing charge q_​1  from infinity to r_​1 is zero because there is no potential in absence of electrical field.
Work done in bring the charge q₂from infinty to r₂  against the field due to charge  q₁ is = q₁V
where V  is potential at point r₂ due to the charge q₁.

As, V= q₁/4$\pi \epsilon$₀r₁₂
 
where 'r₁₂' is the distance between charge 'q₁ ' and 'q₂ '.

 Therefore potential energy of the system is given by the total work done in bring the two charges from infinity to their respective points.

U = 0 + q₂q₁/4$\pi \epsilon$₀r₁₂

U = q₂q₁/4$\pi \epsilon$₀r₁₂