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.

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 distance r from the sheet
Φ = E.ΔScosθ ≈ Φ = E.ΔS (θ=0) ———-(1)
and Φ = σ/εo ———-(2)
From equation (1) and (2)
E = σ/εo × ΔS
E = σ/2εo
We know that,
W = F.r
W = q. σ/2εo. r