# 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 , q2​, 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

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