Two large conducting plates are placed parallel to each other with a separation `d`. An electron `(-e ,m)` starting from rest near one of the plates reaches the other plate in time `t_(0)`. Find the surface density on the inner surface.

Explanation

The electric field between the plates is uniform and is
`E = (sigma)/( 2 in_(0)) + (sigma)/(2 in_(0)) = (sigma)/(in_(0))`
Force on electron `F = eE = (e sigma)/(in_(0))`
Acceleration of electron `a = (F)/(m) = ( e sigma)/( in_(0) m)`
The electron moves from `②` to `①`
`s = ut + (1)/(2) at^(2)`
`d = 0 + (1)/(2) (e sigma)/(m in_(0)) t_(0)^(2)`
`sigma = (2m in_(0) d)/(et_(0)^(2))`