Obtain Gauss's law from Coulomb's law.

Explanation

Coulombian force acting between charges Q +q is,
`F = 1/(4pi epsilon_(0)).(Qq)/r^(2)`
`F/Q =q/(4pi epsilon_(0).r^(2))`
But, `F/Q =vecE`
[Force acting on Q charge placed in electric field of q means intensity of electric field E]
`therefore E = 1/(4pi epsilon_(0)).q/r^(2)`
`therefore E xx 4pir^(2) =q/epsilon_(0)`
`therefore intEds = q/epsilon_(0)`, where `4pir^(2) = ds`
As E and ds are vectors.
`intvecE.vec(ds) =q/epsilon_(0)`. This is Gauss.s law.