The discussion centers on the relationship between Gauss' Law and the Gauss Divergence Law, specifically whether Gauss' Law can be derived from the latter. It is established that while the volume integral of the divergence of the electric field (∇·E) is proportional to the total charge (Q) enclosed, the integrands must be equal, leading to the conclusion that div E equals charge density divided by ε₀. Additionally, the singularity in the electric field at r=0 must be considered in this context.
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There's a singularity in ##\vec{E}## at r=0 you need to account for.nenyan said:Homework Statement
Gauss Divergence Law:
Gauss' law
Can we obtain the Gauss' Law from Gauss Divergence Law?
Homework Equations
In Spherical coordinates,
electric field strength
(Q/4\piεr^2,0,0)
Then ∇\cdotE=0+0+0=0
The Attempt at a Solution
We can not obtain the Gauss' Law from the general mathematical law?