I Why does Gauss' law hold for any closed surface?

AI Thread Summary
Gauss' law applies to any closed surface due to the fundamental relationship between electric flux and charge enclosed, which is mathematically derived from Maxwell's equations. The law states that the total electric flux through a closed surface is proportional to the enclosed charge, regardless of the surface shape. The derivation typically begins with the assumption of electrostatic conditions and the inverse-square law for point charges. Resources like Chapter 1 of "Classical Electrodynamics" by J. D. Jackson provide detailed mathematical proofs. For further exploration, searching for "proof of Gauss law" yields various informative sources and discussions.
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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