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A capacitor is made of two circular plates

Question:

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 a centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is m.

Solution:

When the conducting disc is placed at the centre of the bottom plate, the potential of the disc is equal to the potential of the plate. The electric field on the disc is given as

E = V/d

The charge q’ is transferred to the disc which is given as

q’ = -ε0 V/d πr2

The force acting on the disc is

F = ε0 V2/d2 πr2

Therefore, V = square root of mdg/ π ε0r2

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