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**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.