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A capacitor is made of two circular plates of radius R each, separated by a distance d < < R. The capacitor is connected to a constant voltage. A thin conducting disc of radius r < < R and thickness t < < r is placed at the center of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is m.

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The thin conducting disc of radius r and thickness t is placed at the center of the bottom plate. Therefore, the potential of that thin disc is equal to the potential of that plate.

Hence, the electric field E on the disc will be


Therefore, the charge transferred to the disc

q'=-\varepsilon _{0}\frac{V}{d\; \pi r^{2}}

Therefore, the force acting on the disc,

F=\varepsilon _{0}\frac{V^2}{d^2}\pi r^{2}


V=\sqrt{\frac{md^2g}{\pi \; \varepsilon _{0}r^{2}}}

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