{"knowledge_schema": {"broad_category": "Mathematics \u2192 Vector Calculus \u2192 Surface Integrals", "refinement": "This problem involves evaluating a surface integral of a vector field over a closed surface, specifically using the Divergence Theorem.", "specific_scope": "The vector field given is \ud835\udc05(\ud835\udc2b) = \ud835\udc2b/r^3, and the closed surface is a cube centered at the origin.", "goal": "Determine the value of the surface integral of the vector field over the closed surface."}, "summary": "In this problem, we are tasked with evaluating the surface integral of the vector field \ud835\udc05(\ud835\udc2b) = \ud835\udc2b/r^3 over a closed surface, which is a cube centered at the origin. By applying the Divergence Theorem, we can analyze the divergence of the vector field. Since the divergence of \ud835\udc05 is zero everywhere except at the origin (where it is undefined), and the cube does not enclose the origin, the surface integral evaluates to zero. Thus, the result of the integral is 0."}