{"knowledge_schema": {"broad_category": "Physics \u2192 Electrostatics \u2192 Potential Energy of Charge Distributions", "refinement": "This problem involves calculating the potential energy of a system consisting of a point charge and a grounded conducting sphere, taking into account the effects of induced charges on the sphere.", "specific_scope": "The focus is on determining the net potential energy when a charge is placed at a distance from the center of a grounded conducting sphere, using the principles of electrostatics and the method of images.", "goal": "Calculate the net potential energy of the system formed by the point charge and the grounded conducting sphere."}, "summary": "This problem is rooted in electrostatics, specifically in calculating the potential energy of a system involving a point charge and a grounded conducting sphere. The method of images is typically used to simplify the analysis by replacing the grounded sphere with an equivalent charge configuration. The goal is to find the net potential energy of the system, which can be expressed in terms of the charge, distance, and radius of the sphere. The candidates provided represent different potential energy expressions, and the correct one must be identified based on the principles of electrostatics."}