(Solution) - A negatively charged particle -(2025 Original AI-Free Solution)

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A negatively charged particle -q is placed at the center of a uniformly charged ring, where the ring has a total positive charge Q as shown in Example 23.8. The particle, confined to move along the x axis, is displaced a small distance x along the axis (where x << a) and released. Show that the particle oscillates in simple harmonic motion with a frequency given by