Coulomb's Low And Dirac Delta Functio

[life engineer]

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.

 

[life engineer]

Hey guys I can use a little help here. Just give me a hint.I really really need ur help

 

[Galileo]

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

\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'

Show what you have done so far. Ofcourse, you should know what the charge density of a point particle looks like.

 

[life engineer]

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 don't know the charge density for the point charge and because I don't know a lot 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 don't know how Can u help me please?

 

[Galileo]

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