Electric Flux:
The electric flux through a small surface \vec{ds} is given by;
d\phi = \vec{E} \cdot \vec{ds}
Where, \vec{E} is the electric field through the surface \vec{ds}.
And the electric flux through a surface of the area s is given by;
\phi = \oint_s {\vec{E} \cdot \vec{ds}}
Gauss’s Law:
Gauss’s law for electrostatics is the simplest method to find the electric field at any point near a charge distribution. It states that;
the total electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of the medium.
For a vacuum medium, electric flux through a closed surface is given by;
\phi = \dfrac {q_{en}}{\epsilon_0}
Where,
- q_{en} is the charge enclosed through the closed surface, S,
- \epsilon_0 is the permittivity of the vacuum, and
- \epsilon_0 = 8.854 \times 10^{-12} \rm \ C^2/Nm^2