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Consider an electron in front of the metallic surface

Question:

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 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].

Solution:

The figure shows that an electron is displaced slowly. The distance covered by the electron is x and this happens by the means of an external force

F = q2/4×4πε0d2

d = 0.1 nm = 10-10 m

Let x be the distance of the electron and the force of attraction on it be

Fx = q2/4×4πε0d2

Therefore, work done by the external force is integral of force from d to infinity.

Therefore, work done = 3.6 eV

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