{"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 specific distance from 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 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 scenario requires understanding how the presence of the charge induces a distribution of charge on the sphere, which affects the overall potential energy. The goal is to derive the expression for the net potential energy, which is given by U = - (1/2) * kq^2 R/(4d^2 - R^2). This involves applying the method of images to account for the effects of the grounded sphere."}