How correct is deriving Coulomb's Law from Gauss's Law

[Steenrod]

How correct is "deriving" Coulomb's Law from Gauss's Law

Homework Statement

Here is a question that appeared in my school question paper: "Derive Coulomb's Law from Gauss's Law."

2. The attempt at a solution

I tried the following:
Consider a Gaussian Sphere or radius $r$

By Gass's law,the surface integral ∫E.dA=q/ε implies (4pi r^2) E =q/ε. Solving for E, we get an expression for E which looks like Gauss's law. However, I feel something is not right here.I would appreciate of someone please told me where I am going wrong.
(My course is not rigorous so I apologise in advance for lack of knowledge)
Thank you.

 

[Muphrid]

Your logic is fine. This is the easy way to derive the electric field of a point charge.