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Question

An infinitely large thin plane sheet has a uniform surface charge density +σ. Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet.

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Solution

Let PQRS is an infinitely plane charged sheet and +σ be the distribution of charge over the sheet.Let the charge q is bringing from infinity to the distance r from the sheet.
Then, Electric field at the distant r from the sheet
ϕ=E.Scosθ
ϕ=E.S(θ=0)----------(1)
and ϕ=σϵo-------------(2)
From equation (1) and (2)
E=σϵo×S
E=σϵo×2
We know that,
W=F.r
W=q.σϵo×2.r

657773_623202_ans_e5eea8afec0a4506a99e61e8be084990.jpg

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