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A capcitor is made of two circular palte...

A capcitor is made of two circular paltes 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 si m.

Text Solution

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As shown in fig, the disc is in touch with the bottom plate. The electric field on the disc is `E = V//d`
Therefore, charge q' transferred to the disc
`q' = C.V = (- (in_(0)A)/(d)) V = -in_(0) (V)/(d) pi r^(2)`
Force acting on the disc, `F = -q'E = (in_(0) (V)/(d) pi r^(2)) (V)/(d) = in_(0) (V^(2))/(d^(2)) pi r^(2)`
If the disc is to lifted, `F ge mg, i.e., in_(0) (V^(2))/(d^(2)) pi r^(2) = mg` (for minimum V)
`V = sqrt((mgd^(2))/(pi in_(0) r^(2)))`
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