{"knowledge_schema": {"broad_category": "Physics \u2192 Electromagnetism \u2192 Electric Fields", "refinement": "This problem involves calculating the electric field generated by a moving point charge, taking into account the effects of its motion and the time delay in the observation of the field.", "specific_scope": "The focus is on determining the electric field at a specific observation point and time, given the position and velocity of the charge at an earlier time.", "goal": "Derive the expression for the electric field E\u20d7 at the observation point r\u20d7 and time t, based on the charge's position and velocity at the earlier time tr."}, "summary": "This problem pertains to the calculation of the electric field produced by a moving point charge, considering the time delay in the field's observation. The task is to derive the electric field expression at a specific point and time, using the charge's position and velocity at an earlier time. The correct expression for the electric field is given by E\u20d7(r\u20d7,t) = q(d\u20d7 - v\u20d7) / (4\u03c0\u03f5_o (d c - d\u20d7. v\u20d7)^2), which accounts for the charge's motion and the distance to the observation point."}