The correct answer is D) using fine sandpaper on a de-energized machine between the brush and the commutator to establish the proper curvature. The reasoning behind this is that when installing new brushes on a DC motor commutator, the goal is to ensure a proper fit and curvature between the brush and the commutator surface. Using fine sandpaper on the de-energized machine allows you to carefully shape the brush to match the curvature of the commutator, ensuring optimal contact and performance. The other options, such as using emery paper, a file, or lapping compounds, are generally not recommended for this task as they may be too aggressive and could damage the commutator surface. The key is to use a gentle, controlled approach with fine sandpaper to achieve the desired fit and curvature.