Why does Gauss' law hold for any closed surface?

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SUMMARY

Gauss' law is universally applicable to any closed surface due to its foundational principles in electrostatics, as detailed in Chapter 1 of "Classical Electrodynamics" by J. D. Jackson. The law states that the electric flux through a closed surface is proportional to the enclosed electric charge. Mathematical proofs and derivations can be found through various resources, including online searches for "proof of Gauss law," which yield numerous relevant discussions and documents.

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  • Understanding of electrostatics principles
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  • Basic knowledge of vector calculus
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  • Study the mathematical derivation of Gauss' law from "Classical Electrodynamics" by J. D. Jackson
  • Research electric flux and its applications in electrostatics
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Students of physics, educators in electromagnetism, and researchers seeking a deeper understanding of Gauss' law and its mathematical foundations.

Physgeek64
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Why does Gauss' law hold for any closed surface? and can you show this mathematically.

Many thanks :)
 
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Chapter 1 in Classical Electrodynamics by J. D. Jackson provides this derivation.
 
Physgeek64 said:
can you show this mathematically.
Starting from what assumptions?

Also, a Google search for "proof of Gauss law" turns up a number of pages which may contain what you're looking for, including a number of previous threads here on PF. :oldwink:
 
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