## 30-second summary

## Gauss’s law

“*Gauss’s law states that the net electric flux through any hypothetical closed surface is equal to 1/ε _{0} times the net electric charge within that closed surface.* “

Gauss’s law is useful for determining electric fields when the charge distribution is highly symmetric.

In choosing the surface, always take advantage of the symmetry of the charge distribution so that E can be removed from the integral.

## About Gauss’s law

In its integral form, Gauss’s law relates the charge enclosed by a closed surface to the total flux through that surface. The precise relation between the electric flux through a closed surface and the net charge Q_{encl} enclosed within that surface is given by Gauss’s law:

where *ε** _{0}* is the same constant (permittivity of free space) that appears in Coulomb’s law. The integral on the left is over the value of E on any closed surface, and we choose that surface for our convenience in any given situation. The charge

*Qencl*is the net charge enclosed by that surface.

It doesn’t matter where or how the charge is distributed within the surface. Any charge outside this surface must not be included. A charge outside the chosen surface may affect the position of the electric field lines, but will not affect the net number of lines entering or leaving the surface.

## Application of Gauss’s Law

Gauss’s law is useful for determining electric fields when the charge distribution is highly symmetric. In choosing the surface, always take advantage of the symmetry of the charge distribution so that E can be removed from the integral.

In order to apply Gauss’s law, however, we must choose the “gaussian” surface very carefully so we can determine E. We normally try to think of a surface that has just the symmetry needed so that E will be constant on all or on parts of its surface.

Frequently asked questions

**What is the main application of Gauss’s law?**

Gauss’s law is useful for determining electric fields when the charge distribution is highly symmetric. In choosing the surface, always take advantage of the symmetry of the charge distribution so that E can be removed from the integral.

**Which law is analogous to Gauss’s law.**

Like Ampere’s law, which is analogous to magnetism, Gauss’ law is one of four Maxwell’s equations (the first) and thus fundamental to classical electrodynamics.

**What is the unit of electric charge?**

The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. The coulomb was defined as the quantity of electricity transported in one second by a current of one ampere: 1 C = 1 A × 1 s