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. 

Answer 1

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. ΔScosθ
∴ Φ = E. ΔS(θ = 0)                        .......(1)
and Φ = `σ/∈_0`                            .......(2)
From equation (1) and (2)
E = `σ/[ ∈_0 xx ΔS ]`   

E = `σ/[ ∈_0 xx 2 ]`   

We know that,
W = F.r
W = q . `σ/[ ∈_0 xx 2 ]`.r