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A capacitor is made of two circular plat...

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

A

`(sqrt(mgd))/(pi epsi_(0)r^(2))`

B

`sqrt((mgd)/(pi epsi_(0)r))`

C

`sqrt((m gd^(2))/(pi epsi_(0)r^(2)))`

D

`sqrt((mgd)/(pi epsi_(0)r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
AS shown in figure , the disc is in touch with the bottom plate. The electric field on the disc is `E = V//d` Therefore , charge q transeferred to the disc.
`q = CV = ((epsi_(0)A)/(d)) V = epsi_(0) (V)/(d) pi r^(2)`
Force acting on the disc , `F = q E = (epsi_(0).(V)/(d)pir^(2)) (V)/(d)`
`F = epsi_(0)(V^(2))/(d^(2)) pir^(2)`
If the disc is to be lifted `F ge mg`
`i.e., epsi_(0)(V^(2))/(d^(2))pir^(2) = mg `
(for minimum V)
` therefore sqrt((mgd^(2))/(pi epsi_(0)r^(2)))`
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