Consider an electron in front of metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as `1/4 (q^(2))/(4pi in_(0)d^(2))`.
Calculate work in taking the charge to an infinite distance from the plate. Taking d=0.1nm, find the work done in electron volts. [Such a force law is not valid for d lt 0.1nm].

Explanation

According to question, consider the figure given below From figure, `d=0.1nm=10^(-10)m,`
Let the electron be at distanfce x from metallic surface. Then, force of attraction on it is
`" "F_(x)=(q^(2))/(4xx4piepsi_(0)x^(2))`
Work done by external agency in taking the electron from distance d to infinity is
`" "W=int_(d)^(oo)F_(x)dx=int_(d)^(oo)(q^(2)dx)/(4xx4piepsi_(0))1/x^(2)`
`" "=(q^(2))/(4xx4piepsi_(0))[(1)/(d)]`
`" "=((1.6xx10^(-19))^(2)xx9xx10^(2))/(4xx10^(-10))J`
`" "=((1.6xx10^(-19))^(2)xx(9xx10^(9)))/((4xx10^(-10))xx(1.6xx10^(-19)))eV=3.6eV`