Solving for Charge Position from Flux and Gaussian Surface

[Alem2000]

I was a bit confused by a homwork problem that I was working on. The problem is that I found the flux of a charge and I know the demsions of the Gaussian surface it is encolsed in. It doesn't seem right intuitively to be able to find the location of the charge from this information...but mathmatically I am thinking I can solve for r.
\Phi=\oint _\mathcal{S} \mathbf{E}\cdot d\mathbf{a} = \frac{q_{enc}}{\epsilon _0}
and since electric field is the flux over the area i can find it by
E=\Phi/A
so shouldn't I be able to find the position fo the charge from
\Phi/A=q/4\pi r^2 \epsilon_0
this is really confusing, do I have the theory wrong?

 

[Crosson]

Yes, you have two different definitions for flux:

\Phi = E A

and

\Phi=\oint \vec{E}\cdot \vec{da}

Notice how the second definition is a generalization of the first one. The first equation only applies to flat surfaces which are perpendicular to the field, the second definition works in general.

Also, the r that you pulled out of Gauss' law is the radius of a spherical Gaussian surface (an hence the place you are looking at the field) , not "the distance to the charge".

 

[Alem2000]

THANK YOU, that makes a lot more sense now!