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

In summary, the conversation discusses the process of deriving Coulomb's Law from Gauss's Law. The speaker shares their attempt at solving the question and mentions using a Gaussian Sphere and the surface integral to derive an expression for the electric field. However, they express uncertainty and ask for clarification or correction. The other person reassures them that their logic is correct and this is a common method for deriving the electric field of a point charge.
  • #1
Steenrod
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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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  • #2


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

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

1. How is Coulomb's Law derived from Gauss's Law?

Coulomb's Law can be derived from Gauss's Law by considering a point charge and a Gaussian surface enclosing the charge. By applying Gauss's Law to the surface, the electric field at any point outside the surface can be calculated. The result is equivalent to Coulomb's Law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges.

2. Is it possible to derive Coulomb's Law from Gauss's Law using a different approach?

Yes, it is possible to derive Coulomb's Law from Gauss's Law using other methods such as the integral form of Gauss's Law or vector calculus. However, the most commonly used method is through the use of Gaussian surfaces.

3. How accurate is the derivation of Coulomb's Law from Gauss's Law?

The derivation of Coulomb's Law from Gauss's Law is considered to be very accurate. Gauss's Law is a fundamental principle in electromagnetism and has been extensively tested and verified through experiments. Therefore, any results derived from it, including Coulomb's Law, are considered to be highly accurate.

4. Can Coulomb's Law be derived from Gauss's Law in all situations?

Yes, Coulomb's Law can be derived from Gauss's Law in all situations where there is a static electric field and the charges are at rest. However, if there are moving charges or changing electric fields, other laws and principles must be considered.

5. Why is it important to understand the derivation of Coulomb's Law from Gauss's Law?

Understanding the derivation of Coulomb's Law from Gauss's Law helps to provide a deeper understanding of the fundamental principles of electromagnetism and the relationship between electric charges and electric fields. It also allows for the prediction and calculation of electric fields in various situations, which is crucial in many areas of science and technology.

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