State and explain Gauss's theorem in Electrostatics.

Explanation

Statement: The total outward electric flux in air through any closed surface is equal to `(1// epsilon_(0))` times the total charge enclosed by it.
Let `q_(1),q_(2),q_(3)`……………………`q_(n)` be the charge enclosed by a system of discrete charges.
According to gauss theorem
total flux `phi=(1/( epsilon_(0)))sum_(i=1)^(n)q_(i)`
i.e. `phi=(1/( epsilon_(0)))Q`

where `Q=sum_(i=1)^()q_(1)`
Also `phi=E cos theta ( Sigmacds)` where
`Sigma ds` is the effective area through which component of Electric field `E cos theta` does not vanish.