A non-conducting disc of radius a and uniform positive surface charge density `sigma` is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disc, from a height H with zero initial velocity. The particle has `q//m=4 in_0 g//sigma`
(a) Find the value of H if the particle just reaches the disc.
(b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

Answer

(i) H=4 a/3 (ii) `U(y)=2mg+[sqrt(y^(2)+a^(2))-y]mgy`; at equilibrium `(dU)/(dy)=0 => y=a/sqrt(3)`
`(##RES_PHY_ELE_E03_073_A01##)`