In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:The electric flux through any closed surface is proportional to the enclosed electric charge.The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. It is one of the four Maxwell's equations, which form the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law, and vice versa.Gauss's law may be expressed in its integral form,The integral and differential forms are related by the divergence theorem, also called Gauss's theorem. Each of these forms can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge.
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
Gausss 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.
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