Electric Field due to Infinitely Flat, Charged-Plane with a Uniform Charge Density

Gauss's Law Derivation:

• From symmetry the E-field is always perpendicular to the sheet of charge. At any point the components of the E-field parallel to the plane add to zero because the charge is spread uniformly around the charge.
  
  
• The best choice for a Gaussian surface is a cylinder whose axis is perpendicular to the plane.

• Applying Gauss's Law to the cylinder,