A Charge Oscillating Above A Charged Square Plate.

Consider a point charge of mass \(m\) and charge \(q\) in equilibrium at a height \(h\) above a square plate of charge density \(\sigma\) and side \(a = 2h\) in the presence of gravity in equilibrium. The plate is fixed.

Now, the point charge is given a small displacement in vertical displacement. Find an expression for the time period of its oscillations \(T\) in terms of \(h\) and \(g\), and give the value of \(53.72 T\) for \(h = 9m\) and \(g = 9.8 m/s^2\) to the nearest integer

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