Module 2 : Electrostatics
Lecture 7 : GAUSS'S LAW
Field due to an infinite charged sheet with surface charge density $\sigma$
 

Choose a cylindrical Gaussian pillbox of height $h$ (with $h/2$above the sheet and $h/2$below the sheet) and radius $r$.

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The amount of charge enclosed is area times the surface charge density, i.e., $ Q = \pi r^2\sigma$. By symmetry, the field is directed perpendicular to the sheet, upward at points above the sheet and downward for points below. There is no contribution to the flux from the curved surface. The flux from the two end faces is $\pi r^2 \mid E\mid$each,

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