Why is this line of reasoning wrong?

[mjordan2nd]

Homework Statement

A line of charge λ is located on the z-axis. Determine the electric flux for a rectangular surface with corners at coordinates: (0, R, 0), (w, R, 0), (0, R, L), and (w, R, L).

Homework Equations

\phi = \frac{q_{in}}{\epsilon_0}

The Attempt at a Solution

Instead of the surface given, imagine a rectangular surface located a distance R from the wire with length L and width 2w -- this would have twice the area of the surface given above. Now, imagine four such surfaces so that the wire is now in an enclosed box except for at the top and bottom. By Gauss' Law the net flux through these surface would be λL/ε0. Now, since the surface given by the problem is 1/8 of the surface we've created, why can't we say the flux we're asked to find is λL/8ε0 by symmetry?

 

[mjordan2nd]

*Bump*

 

[vela]

Gauss's law applies only to closed surfaces.

 

[mjordan2nd]

Would this not constitute a closed surface -- a rectangular prism. The tops and bottoms I would think shouldn't matter since the electric field points radially outward.

 

[nasu]

So what will be the dimensions of the face adjacent to the first one?
The first one is 2w x L and at a distance R from the wire.
If the face at 90 from this first one is also 2w in width, it will not be symmetric in respect to the wire. If it's 2R in width it won't be identical with the first one.

 

[mjordan2nd]

Aha! I see now. The second face will be w away from the wire, not R. I'm retarded. Thank you.