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

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SUMMARY

The discussion focuses on deriving Coulomb's Law from Gauss's Law using a Gaussian sphere of radius \( r \). The participant correctly applies Gauss's Law, stating that the surface integral \( \int E \cdot dA = \frac{q}{\epsilon} \) leads to the expression \( E = \frac{q}{4\pi r^2 \epsilon} \). This derivation confirms that the logic is sound, as it effectively demonstrates how Gauss's Law can be utilized to arrive at Coulomb's Law for a point charge. The conclusion emphasizes that the approach is valid and serves as a straightforward method for deriving the electric field of a point charge.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field concepts
  • Basic knowledge of integral calculus
  • Concept of electric charge and permittivity (\(\epsilon\))
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  • Study the mathematical derivation of Gauss's Law
  • Explore applications of Gauss's Law in different geometries
  • Learn about the implications of Coulomb's Law in electrostatics
  • Investigate the relationship between electric field and potential energy
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Students in physics, particularly those studying electromagnetism, as well as educators looking to clarify the relationship between Gauss's Law and Coulomb's Law.

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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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