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.
The electric field on the disc is E=V/d Therefore, charge q′ transferred to the disc q′=CV=(dε0A)V=ε0dVπr2 Force acting on the disc, F=q′E=(dε0Aπr2)dV F=ε0d2V2πr2 If the disc is to be lifted, F≥mg i.e., ε0d2V2πr2=mg (for minimum V) ∴V=√mgd2/πeo r2
