Question

What is the flux on an infinite line of charge?

Answer 1

Flux is only measured and defined for a surface. If you insist on thinking of the line as a surface, then it is a surface with zero surface area and corresponding, the flux is also zero.

Answer 2

I know, I mean from a certain distance r on a cylinder...
\[\Phi = \int\limits\limits\limits_{}^{} E dA = Q _{enc} / \epsilon _{0} \]
\[\lambda = Q / l \]
\[\Phi = E(2 \pi rl) = Q _{enc} / \epsilon _{0}\]
\[\ E = \lambda l / (\ 2 \epsilon _{0} \pi rl)\]

Answer 3

right, and notice that \( \ell \) cancels. This is the calculation of the electric field, and you've got it.