Gaussian Surface

A Gaussian Surface is a closed surface which exhibits Gaussian symmetry.

Gaussian Symmetry: Guarantees that my surface (given by the normal vector $d\vec{S}$) is

1. always perpendicular to or parallel to $\vec{E}$
2. $\vec{E}$ is always the same magnitude everywhere.

Danger

We have to look for symmetry for all charges, not just inside the gaussian surface.

3 Types of Gaussian Surface

• Gaussian Sphere
• Gaussian Cylinder
• Pillbox shape (you can just use a cylinder, but a rectangular shape works as well, or any shape).
  • Make sure the electric field is always perpendicular or parallel to the shape