An infinitely large plate of surface charge density `+sigma` lying in horizontal xy plane. A particle having charge `-q_(0)` and mass m is projected from the plate with velocity u making an angle `theta` with sheet. Find :

(i) the time taken by the particle to return on the plate.
(ii) maximum height achieved by the particle.
(iii) At what distance will it strike the plate (Neglect gravitational force on the particle)

Explanation

Electric force acting on the particle
`F_(e) = q_(0)E : F_(e) = (q_(0))((sigma)/(2 epsilon_(0)))` downward
So acceleration of the particle :
`a = (F_(e))/(m) = (q_(0) sigma)/(2epsilon_(0)m)` = uniform
this acceleration will act like 'g'
(acceleration due to gravity)
So the particle will perform projectile motion.
(i) `T = (2u sin theta)/(g) = (2u sin theta)/(((q_(0) sigma)/(2epsilon_(0)m)))`
(ii) `H = (u^(2) sin^(2) theta)/(2g) = (2u^(2) sin^(2) theta)/(2((q_(0) sigma)/(2epsilon_(0)m)))`
(iii) `R = (u^(2) sin 2 theta)/(g) = (u^(2) sin 2 theta)/(((q_(0) sigma)/(2epsilon_(0)m)))`