Electrix flux through a tetrahedron

[kt7888]

Homework Statement

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)

Homework Equations

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?
Please Help!

 

[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)

 

[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?

 

[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.

 

[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?

 

[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.

 

[kt7888]

Thank you!
Thank you!
Thank you!

I was over-thinking the problem.