Question

How do we consider a Gaussian surface perfectly in order to avoid integration?

Answer 1

A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field , the electric field, or magnetic field.

Gaussian surfaces are usually carefully chosen to exploit symmetries of a situation to simplify the calculation of the surface integral.

There is no laid out way to find Gaussian surface, it varies from question to question. Here are a few common Gaussian surfaces. Spherical surface

A spherical Gaussian surface is used when finding the electric field or the flux produced by any of the following:

• a point charge
• a uniformly distributed spherical shell of charge
• any other charge distribution with spherical symmetry

The spherical Gaussian surface is chosen so that it is concentric with the charge distribution.

Cylindrical surface

A cylindrical Gaussian surface is used when finding the electric field or the flux produced by any of the following:

• an infinitely long line of uniform charge
• an infinite plane of uniform charge
• an infinitely long cylinder of uniform charge

Gaussian pillbox

This surface is most often used to determine the electric field due to an infinite sheet of charge with uniform charge density, or a slab of charge with some finite thickness.