Explain Electric Potential Energy with Equation

The electric potential energy of two point charges is equal to the work done to assemble the charges or work done in bringing each charge or work done in bringing a charge from the infinite distance.

Let consider a point charge q₁, placed at A (Figure].

The potential at a point B at a distance r from the charge q₁ is

V = q₁/(4πε₀r)

Another point charge q₂ is brought from infinity to the point B.

Now the work done on the charge q₂ is stored as electrostatic potential energy (U) in the system of charges q₁ and q₂.

work is done w = Vq₂

Potential Energy: (U) = q₁q₂/(4πε₀r)

Keeping q₂ at B, if the charge q₁ is imagined to be brought from infinity to the point A, the same amount of work is done.

Also, if both the charges q₁ and q₂ are brought from infinity, to points A and B respectively, separated by a distance r, the potential energy of the system is the same as the previous cases.

For a system containing more than two charges, the potential energy (U) is given by

U = 1/(4πε₀) * [(q₁q₂/r₁₂) + (q₁q₃/r₁₃) + (q₂q₃/r₂₃)]