Hi. Consider the cylindrical Gaussian surface (Gs) shown in the following picture: Using Gauss's law, ∫ E ⋅ dA= E ∫ dA = Q/ ε E 2 π r L = λ L / ε E= λ /(2 π r ε) Is this true? I have a feeling like this is wrong. We have considered that there is only ONE electric field vector, E, fluxing through each da on Gs. Now, consider a infinitesimally small area on Gs, call it da. There are too many electric field vectors that we can construct, since there are infinitely many charge on the line/wire (superposition of electric flux through a surface). I mean, there can also be a electric field (say E') vector that is not parallel to the vector of da: da and E vectors ∧ | \ | \ ← E' | \ | \ -------- ←edge-on view of da (a part of Gs) | \ | \ +-----------+ ←another charge on the line/wire which has electric field vector that is not parallel to the vector da. Then the total E flux through the da on Gs is the superposition of all electric flux through it due to every charge on the line/wire. Can you see where I'm wrong? P.S. : Unfortunately, the diagram that I typed can't be view correctly after posting.... hope that you can get what I mean anyway. Just give some space between each " | " and " \ " so that you can see a triangle (a vector diagram with the base's edge replaced by "+" charge). Thanks.