Confused about Flux

[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!