{"knowledge_schema": {"broad_category": "Physics \u2192 Electromagnetism \u2192 Dielectric Materials", "refinement": "This problem involves the behavior of electric fields and potentials in the presence of dielectric materials with different permittivities and conductivities.", "specific_scope": "The focus is on determining the electric potential and electric field around a dielectric sphere placed in a uniform electric field, considering the steady-state conditions and the properties of the materials involved.", "goal": "To 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) and inside the sphere (r < R) under the influence of an external electric field."}, "summary": "This problem deals with the electric potential and electric field around a dielectric sphere in a uniform electric field. It requires understanding the effects of different dielectric permittivities and conductivities on the electric field and potential in both the interior and exterior of the sphere. The goal is to derive the expressions for the electric potential and electric field in both regions, ensuring that the solutions satisfy the boundary conditions and the steady-state conditions of the system."}