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What is Gauss's theorum?
This theorem gives a relation between the total flux through any surface and net charge enclosed within the surface.According to Gauss's theorem the net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed with in that closed surface.Gauss's law may be expressed as
\Phi_E = \frac{Q}{\varepsilon_0}
where ?E is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within S, and ?0 is the electric constant. The electric flux ?E is defined as a surface integral of the electric field.
\Phi_E = \oiint{\scriptstyle S}\mathbf{E} \cdot \mathrm{d}\mathbf{A}

where E is the electric field, dA is a vector representing an infinitesimal element of area 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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