In this section, we examine the potential energy of a system of two charges in the context of an external electric field. The potential energy of two charges, denoted as q₁ and q₂, can be calculated based on the work done to assemble this system from infinity, wherein no initial work is needed for the first charge (q₁). The work done in bringing the second charge (q₂) to its position includes both the influence of the external electric field V(r₂) and the potential energy contribution from the interaction of the charges themselves. The mathematical expression that encapsulates this relationship is:
U = q₁V(r₁) + q₂V(r₂) + (q₁q₂)/(4πε₀r₁₂),
where r₁₂ is the distance between the two charges. This relationship underscores the principle of superposition in electric fields, as well as the conservative nature of the electrostatic force at play. The potential energy is a significant concept as it ultimately relates to the dynamics of the charges within the field, influencing how they will behave when released.