Can Gauss' Law be applied to point charges on non-spherical surfaces?

[manenbu]

2 questions:

1. A point charge of 1.84 microC is at the center of a cubical Gaussian surface 55cm on edge. Find $\Phi_E$ through the surface.

So here I was thinking, well the shape doesn't matter so the surface can be a sphere, so I calculated it for a sphere and it was correct (taking the radius as half of the edge).
But - how to do it for a square?

2. This one is related too - being "A point charge +q is a distance d/2 from a square surface of side d and is directly above the center of the square. Find the flux through the square".

More or less the same, solve with letters instead of numbers and divide by six. Again - how to do it without turning it into a sphere?

 

[zhermes]

I think the best way to understand this is to think about what gauss' law says.

The equation is (of course):
$$\oint \vec{E} d\vec{A} = \frac{q_{inc}}{\epsilon_0}$$
But what does this mean?

 

[manenbu]

It means that the flux is equal to the charge inside the surface over e0.
Ok. It came to me now. :)