Gauss's theorem, the fundamental theorem of electrostatics, which relates the flux of the electric field strength E through a closed surface S to the magnitude of the charge q contained inside that surface. In the Gaussian system of units
div E=4πq. (1)
Gauss's theorem follows from Coulomb's law. In a dielectric, Gauss's theorem holds for the flux of the electric induction vector D:
divD=4πq, (2)
where q is the total free charge inside the surface S. Formula (2) is the integral form of one (the fourth) of Maxwell's equations for the electromagnetic field, and it expresses the fact that electric charges are the sources of the electric field.
div E=4πq. (1)
Gauss's theorem follows from Coulomb's law. In a dielectric, Gauss's theorem holds for the flux of the electric induction vector D:
divD=4πq, (2)
where q is the total free charge inside the surface S. Formula (2) is the integral form of one (the fourth) of Maxwell's equations for the electromagnetic field, and it expresses the fact that electric charges are the sources of the electric field.