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

AI Thread Summary
Deriving Coulomb's Law from Gauss's Law involves using a Gaussian sphere to calculate the electric field. By applying Gauss's Law, the surface integral leads to the equation (4πr²)E = q/ε, allowing for the calculation of the electric field E. The derivation is considered valid and is a straightforward method to find the electric field of a point charge. Concerns about rigor in the course material are acknowledged, but the logic of the derivation is sound. Overall, the approach effectively demonstrates the relationship between the two laws.
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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.
 
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Your logic is fine. This is the easy way to derive the electric field of a point charge.
 

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