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Coulomb's Low And Dirac Delta Functio

  1. Sep 30, 2005 #1
    I want to prove coulomb's low for a single charge point from the general form of coulomb's low:
    E→=1/(4∏€) ∫∫∫ ρv(ŕ) * (r→- ŕ→)/│(r→- ŕ→)│^3 dŕ
    using Dirac Delta function
    where r→ is the field point vector
    ŕ→ is the source point vector
    ρv(ŕ) is the volume charge density
    I really don't know how to do it . I tried a lot but couldn't do it so can u help me please as soon as possible.Just guide me how to do it.
  2. jcsd
  3. Oct 1, 2005 #2
    Hey guys I can use a little help here. Just give me a hint.I really really need ur help
  4. Oct 1, 2005 #3


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    The equation looks messed up (try LaTeX), but I guess you mean:

    [tex]\vec E(\vec r)=\frac{1}{4\pi \epsilon_0}\int_V \frac{\rho(\vec r')}{|\vec r-\vec r'|^3}(\vec r-\vec r')dV'[/tex]

    Show what you have done so far. Ofcourse, you should know what the charge density of a point particle looks like.
  5. Oct 1, 2005 #4
    yes ur guess is right the equation u wrote is the one I meant . yet I didnt reach any thing that make sense. I guess because I dont know the charge density for the point charge and because I dont know alot about dirac delta function. I know it converts continuous functions into discreete ones Ithink this is the main idea of the solution but yet I dont know how Can u help me plz?
  6. Oct 2, 2005 #5


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    Ofcourse, you should read up on what the dirac delta function is before using it to solve anything. I`m sure there's a discussion about it in your book.
    http://planetmath.org/encyclopedia/DiracDeltaFunction.html [Broken]
    Last edited by a moderator: May 2, 2017
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