Gauss's law

Gauss's law states that the electric flux through any closed surface equals the enclosed electric charge divided by the vacuum permittivity. It is one of Maxwell's equations.

Electric flux: A measure of how much electric field passes through a surface, calculated from the field’s normal component. It is the quantity Gauss's law integrates across a closed surface.
Coulomb's law: The law giving the electrostatic force between two point charges as proportional to their product and inversely proportional to distance squared. For point charges, it gives the field that Gauss's law can also recover using spherical symmetry.
Electric field: A vector field that gives the electric force per unit positive test charge at each point. Gauss's law relates this field's flux to the charge enclosed by a surface.
Differential form of Gauss's law: The local equation stating that electric-field divergence equals charge density divided by vacuum permittivity. It expresses the same law point by point rather than over a closed surface.
Gaussian surface: An imagined closed surface used to apply Gauss's law to an electric-field problem. Choosing a surface that matches the charge symmetry can simplify the flux calculation.
Spherical symmetry: A symmetry in which a system is unchanged by rotations about a central point. It makes the field uniform over spherical Gaussian surfaces around a point charge or charged sphere.
Closed surface: A surface that completely encloses a volume and has no boundary edge. The law requires a closed boundary so its enclosed charge is well-defined.
Gauss's law in matter: A macroscopic form of Gauss's law relating electric displacement flux to free charge. It distinguishes free charge from bound charge when fields in materials are treated.
Enclosed charge: The net electric charge contained within a specified closed surface. Gauss's law relates this charge directly to the surface's total electric flux.
Infinite line charge: An idealized straight line carrying uniform electric charge along its entire infinite length. A cylindrical Gaussian surface reduces its field calculation to one unknown radial magnitude.

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