Gauss' law and flux concept issues

[engineeringstudnt]

Homework Statement

Gauss's law and flux concept issues

Relevant Equations

flux=Qenclosing/Epsilon

Hi guys i have some concept issues about flux. My book says flux is proportional to the number of lines passing through that area. so my question is: first i am thinking that a 2D circle which has a 2r diameter and it is enclosing a 2q charge so its flux should be 2q/Epsilon.then i am thinking a 3D sphere which have a 2r diamater again. so its flux should be 2q/Epsilon too ,right ?

but how ? isn't the sphere has more electric field lines passing through its area ?

 

[vela]

The Gaussian surface must be a closed surface. A circle in three-dimensional space isn't a closed surface, so Gauss's law won't hold.

 

[engineeringstudnt]

thank you very much i am thinking about this almost 45 minutes :D