Gauss's law : The total electric flux through any closed surface is equal to \(1 / \varepsilon_{0}\) times the net charge enclosed by the surface
Total electric flux,
$$
\phi=\oint_{S} \overrightarrow{\mathrm{E}} \cdot \mathrm{d} \overrightarrow{\mathrm{s}}=\frac{\mathrm{q}}{\varepsilon_{0}}
$$
Here \(q\) is the total charge enclosed by the surface ' \(S\) ', \(\oint\) represents surface integral of the closed surface.
Importance :
(1) Gauss's law is very useful in calculating the electric field in case of problems where it is possible to construct a closed surface. Such surface is called Gaussian surface.
(2) Gauss's law is true for any closed surface, no matter what its shape or size.
(3) Symmetric considerations in many problems make the application of Gauss's law much easier.
