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.

Explanation

Assuming initially the disc is in touch with the bottom plate, so the entire plate is a equipotential the electric field on the disc, when potential difference V is applied across it, given by ltBrgt `E=(V)/(d)`
Let charge q' is transferred to the disc during the process,
therefore by gauss' theorem
`thereforeq'=-epsi_(0)(V)/(d)pir^(2)`
Since, gauss theorem states that `phi=(q)/(epsi_(0))` or `q=(epsi_(0))/(phi)`
`=epsiEA=(epsi_(0)V)/(d)A`
The force acting on the disc is
`-(V)/(d)xxq'=epsi_(0)(V^(2))/(d^(2))pir^(2)`
If the disc is to be lifted then,
`epsi_(0)(V^(2))/(d^(2))pir^(2)=mgimpliesV=sqrt((mgd^(2))/(piepsi_(0)r^(2)))`
this is the required expression.