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  • Consider an electron in front of the metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as 2 2 0 1 4 4 q πε d Calculate work in taking the charge to an infinite distance

Consider an electron in front of the metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as 2 2 0 1 4 4 q \pi\epsilon d 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 < 0.1nm].

 

Answers (1)

Explanation:-

Let us consider the above-given figure wherein an electron is displaced slowly by a distance x by the means of an external force which is given by

F=\frac{q^{2}}{4*4\pi\varepsilon_{0}d^{2}}\; where \;d=0.1nm=10^{-10}m

 Now work done by an external agency in taking the electron from distance d to infinity is

W=\int_{d}^{\infty }F_{x}dx=\int_{d}^{\infty }\frac{q^{2}dx}{4*4\pi\varepsilon _{0}}*\frac{1}{x^{2}}\\\\\\ =\frac{q^{2}dx}{4*4\pi\varepsilon _{0}}\left (\frac{1}{d} \right )=\frac{\left ( 1.6*10^{-19} \right )^{2}}{1.6*10^{-19}}*\frac{\left ( 9*10^{9} \right )}{4*10^{-10}}=3.6eV

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