Gauss’s law is a general statement about the nature of electric fields. It is more fundamental than Coulomb’s law and is the first of what we will later call Maxwell’s equations, the governing equations of electricity and magnetism.

Gauss’s law says that the electric flux through a closed surface is proportional to the amount of charge $Q_{\text{in}}$ enclosed within the surface. This seemingly abstract statement will be the basis of a powerful strategy for finding the electric fields of charge distributions that have a high degree of symmetry.

《 LOOKING BACK Section 22.5 The electric field of a point charge Section 23.2 Electric field lines

For charge distributions with a high degree of symmetry, the symmetry of the electric field must match the symmetry of the charge distribution. Important symmetries are planar symmetry, cylindrical symmetry, and spherical symmetry. The concept of symmetry plays an important role in math and science.

The amount of electric field passing through a surface is called the electric flux. Electric flux is analogous to the amount of air or water flowing through a loop. You will learn to calculate the flux through open and closed surfaces.

《 LOOKING BACK Section 9.3 Vector dot products

Gauss’s law is easier to use than superposition for finding the electric field both inside and outside of charged spheres, cylinders, and planes. To use Gauss’s law, you calculate the electric flux through a Gaussian surface surrounding the charge. This will turn out to be much easier than it sounds!

Gauss’s law can be used to establish several properties of conductors in electrostatic equilibrium. In particular:

• Any excess charge is all on the surface.

• The interior electric field is zero.

• The external field is perpendicular to the surface.