Homework Help: Electrix flux through a tetrahedron

1. Oct 7, 2008

kt7888

1. The problem statement, all variables and given/known data
what is the outward flux through one of the 4 triangular faces of a tetrahedron centered at the origin if the charge density is q*(delta)^3(r)

2. Relevant equations

3. The attempt at a solution
So, I figured that all I had to do was find the point charge q that the tetrahedron encloses....because I can find that by integrating over the charge density....
my problems are...am I making this problem too hard? Is there a simpler way to solve this?
and also, if I integrate over the charge density to, what are the limits of the integral, and how do you integrate the dirac delta?

2. Oct 7, 2008

gabbagabbahey

Use the definition of the dirac delta:

$$\int_{all space} f(\vec{r'}) \delta ^3 (\vec{r}) d^3r'=f(0)$$

So where does this mean the charge q is located? ;0)

3. Oct 7, 2008

kt7888

q would be located at the origin......right?

but, don't I have to know what q is by the charge density?

or is it simply the flux from a point charge at the origin? But if that's the case, where does the charge density come into play?

4. Oct 7, 2008

gabbagabbahey

Yes, it is a point charge q, located at the origin. The charge density just tells you that the only charge is the point charge q at the origin, that's all the information that you need from it. Just calculate the Flux from a point charge at the origin through one face of the tetrahedron.

5. Oct 7, 2008

kt7888

so the flux from a point charge is q/e0

So, since the flux is through a tetrahedron, then it would be q/4e0

right????

6. Oct 7, 2008

gabbagabbahey

Yes, but this is only true because the point charge is at the center of the tetrahedron, and so the flux through each face is equal.

7. Oct 7, 2008

kt7888

Thank you!
Thank you!
Thank you!

I was over-thinking the problem.