Understanding Gauss' Law and E Fields in Flux Calculations

[EV33]

Homework Statement

I actually just have two questions about the law itself.

1.) Is Gauss's Law just the projection of a shape onto a perpindicular surface to the E field,times the E field?

I ask this because there is an example in my book which shows a 3D incline with a horizontal E field, and the flux through the vertical is the same has the flux through the hypotenuse side of the incline. The only difference is that one is EA and the other is E*A*cos(theta).

So under my assumption on flux if there is a horizontal e field, and a half sphere with its flat side perpindicular to the e field, I would assume that the flux would be the same through both the flat and round side.

2.) My question for this one involves E fields involving infinite large planes. If you calculate the e field involving a plane you can do it with the equation
E=sigma/2 epsilon nat, but my question about this is, where does that calculate the E field at. My assumption is that it calculates the E field right at the surface. If this is so and I wanted to find the E field some x distance away, would I just put that E value over X^2, to get the E value at X distance away?

Homework Equations

flux=E(dot)A
Flux=Q enclosed/epsilon nat
E=sigma/2 epsilon nat

The Attempt at a Solution

1.)Well I figured for the half circle that both sides would have to have equal but opposite flux's because if q inside is zero then the net flux for the object needs to be zero, so the neg flux needs to cancel out the pos flux for the other side.

 

[HarleySpirit]

In brief, here are two links that will, I believe, make the difference.
http://en.wikipedia.org/wiki/Gaussian_surface
http://en.wikipedia.org/wiki/Gauss's_Law

 

[HarleySpirit]

Hope this helps. Remember: scalar fields don't ALWAYS obey! But that's the way to bet.