How does Gauss's law simplify to EA for practical problems?

[iRaid]

Hey everyone,
I was wondering if someone could explain Gauss's law. For whatever reason, I just cannot grasp this idea (might be my teacher). I understand that the electric field through a surface can be represented as $\oint \vec{E} d\vec{A}$ but every problem that we do ends up resulting in it equaling $E\oint dA$ and finally EA. I really don't even understand this equation, how to use it, how to apply it, etc. If anyone could clear this up that'd be great.

Thanks.

 

[ANUJ G SHARMA]

Gauss law: the total flux through a surface is (1/$\epsilon$) times the total charge enclosed within it .. we take integral of E.ds to arrive to a equation ie $\phi$ = q/$\epsilon$ .
while integrating consider a point charge and make a guassian surface of a sphere, and you will find that kq/r²*4∏r². now this 4∏r² gets canceled with your k and r²... hence we take integral of that to arrive at equation.

 

[Claude Bile]

The integral form of Gauss's Law is used to work out the charge enclosed by a surface by integrating the electric flux over that surface.

The reason E can frequently be taken outside the integral is that Gauss's Law is independent of the chosen surface. So it makes sense to choose a surface with nice symmetry that makes the integral as simple as possible.

Claude.