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Gauss's Law

• Electric Flux: If a uniform electric field E is perpendicular to a plane of area A, then the electric flux through the area is defined as the product EA. If E makes an angle theta with the normal (perpendicular) to the plane, then the flux is given by EAcos(theta).
• In general, given an electric field E in a certain region of space, and a closed surface, we define the electric flux through the closed surface as a surface integral of the dot product of E and da, where da is a vector with a magnitude equal to the area of the surface element da and whose direction is the outward normal to the surface element da, and E is the electric field at the position of the element da.
• Gauss’s law: The electric flux through any closed surface is equal to Q_enc / epsilon_0, where Q_enc is the charge enclosed within the closed surface, and epsilon_0 = 8.854 x 10^-12 in SI units.