Answer to Question #217473 in Electricity and Magnetism for Pilot

Question #217473
Apply gauss's theorem to calcutta the electric field in the case of a changed infimite plan
1
Expert's answer
2021-07-15T12:48:46-0400

Gaussian surface total output flux


ϕ=s1E.ds+s2E.ds+s3E.ds\phi=\smallint_{s_1}E.ds+\smallint_{s_2}E.ds+\smallint_{s_3}E.ds

s3 surface Eand ds is perpendicular

θ=90°\theta=90°

s3E.ds=s3E.dscosθs3E.dscos90=0\smallint_{s_3}E.ds=\smallint_{s_3}E.dscos\theta\\\smallint_{s_3}E.dscos90=0

s1,s3s_1,s_3 Surface are E and ds are same direction

θ=0°\theta=0°


ϕ=s1E.dscosθ+0+s3E.dscosθϕ=2ES(1)\phi=\smallint_{s_1}E.dscos\theta+0+\smallint_{s_3}E.dscos\theta\\\phi=2ES\rightarrow(1)

Gauss law

ϕ=qϵ0(2)\phi=\frac{q}{\epsilon_0}\rightarrow(2)

Surface charge density

σ=qSq=σS(3)\sigma=\frac{q}{S}\\q=\sigma S \rightarrow(3)

equation (1),(2),(3) we can written as

E=σ2ϵE=\frac{\sigma}{2\epsilon}


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