{"knowledge_schema": {"broad_category": "Physics \u2192 Electrostatics \u2192 Potential Energy of Charge Configurations", "refinement": "This problem involves the interaction between a point charge and a conducting sphere, specifically focusing on the effects of grounding and induced charges.", "specific_scope": "The task is to calculate the total potential energy of a system consisting of a point charge and a grounded conducting sphere, taking into account the distance from the charge to the sphere and the sphere's radius.", "goal": "Determine the expression for the total potential energy of the configuration involving the point charge and the grounded conducting sphere."}, "summary": "This problem is rooted in electrostatics, where we analyze the potential energy of a point charge in the presence of a grounded conducting sphere. The configuration involves understanding how the point charge induces charges on the sphere and how this affects the overall potential energy. The goal is to derive the correct expression for the total potential energy, which is given by U = - (1/2) * kq^2 R / (d^2 - R^2). This expression accounts for the interactions between the charge and the induced charges on the sphere."}