{"knowledge_schema": {"broad_category": "Physics \u2192 Electromagnetism \u2192 Electrostatics in Dielectric Media", "refinement": "This problem involves the analysis of electric fields and potentials in the presence of dielectric materials and conductors, specifically focusing on the behavior of a dielectric sphere in an external electric field.", "specific_scope": "The task is to determine the electric potential and electric field in the region outside a dielectric sphere when subjected to a uniform electric field, considering the properties of the sphere and the surrounding medium.", "goal": "Find the expressions for the electric potential \u03a6(r, \u03b8) and the electric field E\u20d7(r, \u03b8) in the region outside the sphere (r > R) in the steady state."}, "summary": "This problem is centered on understanding the behavior of electric fields and potentials around a dielectric sphere placed in a uniform electric field. The goal is to derive the expressions for the electric potential and electric field outside the sphere, taking into account the dielectric properties and conductivities of both the sphere and the surrounding medium. The solution requires applying principles of electrostatics and boundary conditions to find the correct mathematical representations for the potential and field in the specified regions."}