{"knowledge_schema": {"broad_category": "Physics \u2192 Electrostatics \u2192 Potential Energy of Charged Particles", "refinement": "This problem involves calculating the electrostatic potential energy in a system of charged particles, taking into account their interactions based on Coulomb's law.", "specific_scope": "The focus is on a closed system with 13 charged particles, where 12 are fixed at a distance from a point charge, and one charge is located at that point, requiring the calculation of the total potential energy of the configuration.", "goal": "Determine the minimum electrostatic potential energy of the system of charged particles."}, "summary": "This problem is rooted in electrostatics, specifically in calculating the potential energy of a system of charged particles. It involves 13 identical particles, each with a charge of 2e, where 12 are fixed at a distance of 2 meters from a point charge at Q. The task is to compute the total electrostatic potential energy of this configuration using Coulomb's law. The goal is to find the minimum energy of the system, which is given as 2.822 x 10^-26 Joules."}