# Coulomb's Low And Dirac Delta Functio

1. Sep 30, 2005

### 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.

2. Oct 1, 2005

### life engineer

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

3. Oct 1, 2005

### 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.

4. Oct 1, 2005

### 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 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?

5. Oct 2, 2005

### 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 [Broken]

Last edited by a moderator: May 2, 2017