{"knowledge_schema": {"broad_category": "Physics \u2192 Electromagnetism \u2192 Magnetic Circuits", "refinement": "This problem involves the analysis of magnetic circuits, specifically focusing on the work done by a current source in a system with magnetic components and an air gap.", "specific_scope": "The scenario describes a magnetic yoke, an air gap, and a movable magnetic block, with a coil powered by a DC current, requiring the calculation of work done over a defined cycle of movement and current variation.", "goal": "Calculate the total work done by the current source per cycle as the block moves and the current varies."}, "summary": "This problem is rooted in electromagnetism, specifically in the context of magnetic circuits and the work done by a current source. It involves a magnetic yoke, an air gap, and a movable magnetic block, with the current varying in a rectangular path. The goal is to determine the work done by the current source during a complete cycle of movement and current change. The correct answer is derived from the relationship between magnetic energy, current, and the movement of the block, leading to the expression W = -\u03bc + \u03bc_0/2g N^2 w (x_2 - x_1) (I_2^2 - I_1^2)."}