Gauss' Law

The total electric flux passing out from a closed surface (c.s.) is (in rationalized units) equal to the total charge, q, enclosed within the surface. In unrationalized units, the flux is equal to 4 times the enclosed charge q.

In integral form, Gauss' law may be written (in rationalized MKS units):

where D is the electric flux density, E is the electric field strength, is the electric charge density and is the permittivity of free space.

Applying the Gauss theorem, the law may be put in the differential form,

Using

the law may be put into still another form, the Poisson equation:

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