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Coulomb’s Theorem

Consider a conducting surface of very small surface area δs having charge density of σ coulombs per unit of surface area

Total charge on small surface δs = σδs coulombs.

According to Gauss’s theorem the total flux, ψ  radiating from the charge of σδs coulombs = σδs coulombs.

Since in conducting surface no flux can exist inside and whole of the flux comes outward normally.

Flux density at the surface  =  ψ = σδs = σ
                                          S       δs

Field intensity at any point close to the surface,

E = D    =    σ    N/C
    ∈o∈r     ∈o∈r

Hence according to Coulombs theorem, the electric intensity at a surface of a conducting dy, having a charge density f coulombs per unit of surface area   σ   where  ∈or = E the absolute permittivity of the
  medium surrounding the conductor.

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