# 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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