(Solution) - Show that the maximum values of the electric field E -(2025 Original AI-Free Solution)

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Show that the maximum values of the electric field |E| for points on the axis of a uniform ring of charge q and radius a occur at a distance
x = ± a/?2.
If an electron is placed at the centre of the ring and is then displaced a small distance x along the axis (x << a), show that it oscillates with a frequency
v = ?eq/16?3?0a3m
Where m is the mass of the electron.