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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 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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Explanation:-

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, if we talk about the electric field that is present on a disc, so electric field will be:

 E=\frac{V}{d}

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}

Therefore,

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

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