A Gaussian surface is a closed imaginary surface in three-dimensional space through which the flux of a vector field is calculated. It enclosed all the charges for which flux is to be calculated.
Gauss's Law:
The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813. It is one of Maxwell's four equations, which form the basis of classical electrodynamics.
The net electric flux through any hypothetical closed surface (Gaussian Surface) is equal to ...... times the net electric charge within that closed surface.
Integral Form of Gauss's Law
Gauss's law may be expressed as:
Where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within V, and ε0 is the electric permittivity. The electric flux ΦE is defined as a surface integral of the electric field:
Where E is the electric field, dA is a vector representing an infinitesimal element of area of the surface, and · represents the dot product of two vectors.
Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.
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