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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.
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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