An electron having charge $$e$$ and mass $$m$$ starts from the lower plate of two metallic plates separated by a distance $$d.$$ If the potential difference between the plates is $$V,$$ the time taken by the electron to reach the upper plate is given by

Solution :
$$\eqalign{ & E = \frac{V}{d},F = eE = \frac{{eV}}{d} \cr & a = \frac{F}{m} = \frac{{eV}}{{md}} \cr & d = \frac{1}{2}a{t^2}\,{\text{or}}\,t = \sqrt {\frac{{2\;d}}{a}} \cr & {\text{or}}\,\,t = \sqrt {\frac{{2d\,md}}{{eV}}} = \sqrt {\frac{{2m{d^2}}}{{eV}}} \cr} $$