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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. 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
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