Obtain Gauss law from Coulomb 's law .

Explanation

A positive point charge Q is surrounded by an imaginary sphere of radius r electric flux through the closed surface of the sphere
`Phi_(E)=ointvec(E).dvecA=ointEdAcostheta`
(ii) The electric field of the point charge is directed radially outward at all points on the surface of the sphere. Therefore, the direction of the area element `dvec(A)` is along the electric field `vec(E)` and `theta=0^(@)`.

`Phi_(E)=ointEdA` since `cos0^(@)=1`,
(iii) E is uniform on the surface of the sphere `Phi_(E)=EointdA`
Substituting for `ointdA=4pir^(2)`
`:.phiE=4piepsi_(0).(Q)/(r^(2))`
`E=(1)/(4piepsi_(0)).(Q)/(r^(2))`
`Phi_(E)=(1)/(4piepsi_(0)).(Q)/(r^(2))xx4pir^(2)=4pi(1)/(4piepsi_(0))Q`
`Phi_(E)=(Q)/(epsi_(0))`
The equation is called as Gauss.s law.