1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    df53cbd418aaded3f2ad2d2fe1d60f2d.png
    Gauss' law
    914f57946de3c30d15e1a9778b276842.png

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

    2. Relevant equations

    In Spherical coordinates,

    electric field strength

    (Q/4[itex]\pi[/itex]εr^2,0,0)
    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

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    There's a singularity in ##\vec{E}## at r=0 you need to account for.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to deduce Gauss' law from Gauss Divergence Law
Loading...