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Homework Help: How to deduce Gauss' law from Gauss Divergence Law

  1. Oct 28, 2013 #1
    1. The problem statement, all variables and given/known data
    Gauss Divergence Law:
    Gauss' law

    Can we obtain the Gauss' Law from Gauss Divergence Law?

    2. Relevant equations

    In Spherical coordinates,

    electric field strength

    Then ∇[itex]\cdot[/itex]E=0+0+0=0

    3. The attempt at a solution

    We can not obtain the Gauss' Law from the general mathematical law?
  2. jcsd
  3. Oct 28, 2013 #2


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    So the volume integral of div E [application of Gauss' theorem to Gauss' law) is proportional to Q, the total charge included.

    But Q is the volume integral of the charge density ... so we have a volume integral on both sides.

    Then the integrands must be equal, which gives div E = densit/eps_0.
  4. Oct 28, 2013 #3


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    Staff Emeritus
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    There's a singularity in ##\vec{E}## at r=0 you need to account for.
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