Question

Use Gauss’s theorem to calculate the electric field due to an infinite plane sheet of charge ​

Answer 1

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Consider a thin infinite plane sheet of charge with uniform surface charge density σ. To calculate electric field at point P at a distance 'r' from it. We choose cylindriy Gaussian surface of cross-sectional area A and length 'dr' with it's axis perpendicular to the sheet.

As, σ = q/A .................(1)

(See Attachment because it is difficult to write e.g. integration, etc.)

Now, According to Gauss Theorem,

see 2nd attachment

E = σ/2(epselon not)