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

`d=0.1nm =10^(-10)m , F=(q^(2))/(4xx4pi in_(0)d^(2))`
Let the electron be at distance x from metallic surface. Then force of attraction on it is
`F_(x)=(q^(2))/(4xx4pi in_(0)x^(2))`
Work done by an external agency for a displacement dx against the force of attraction `F_(x)` is,
`dW=F_(x)dx`
Total workdone 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)/(4xx4pi in_(0)x^(2))=(q^(2))/(4xx4pi in_(0))[1/d]`
`=((1.6xx10^(-19))^(2)xx9xx10^(9))/(4xx10^(-10))J=((1.6xx10^(-19))^(2)xx(9xx10^(9)))/((4xx10^(-10))xx(1.6xx10^(-19)))eV=3.6eV`