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

  1. Sep 6, 2012 #1
    How correct is "deriving" Coulomb's Law from Gauss's Law

    1. The problem statement, all variables and given/known data
    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.
     
  2. jcsd
  3. Sep 6, 2012 #2
    Re: How correct is "deriving" Coulomb's Law from Gauss's Law

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