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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.
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Solution
When the disc is in touch with the bottom plate, the entire plate is a equipotential. A change q′ is transferred to the disc.
The electric field on the disc is `V/d`
∴ q' = `ε_0 V/d pir^2`
The force acting on the disc is `- V/d xx q^' = ε_0 V^2/d^2 pir^2`
If the disc is to be lifted, then `ε_0 V^2/d^2 pir^2 = mg`
⇒ V = `sqrt((mgd^2)/(piε_0r^2))`
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