Gaussian surface total output flux
ϕ=∫s1E.ds+∫s2E.ds+∫s3E.ds s3 surface Eand ds is perpendicular
θ=90°
∫s3E.ds=∫s3E.dscosθ∫s3E.dscos90=0
s1,s3 Surface are E and ds are same direction
θ=0°
ϕ=∫s1E.dscosθ+0+∫s3E.dscosθϕ=2ES→(1) Gauss law
ϕ=ϵ0q→(2)
Surface charge density
σ=Sqq=σS→(3)
equation (1),(2),(3) we can written as
E=2ϵσ
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