# Symmetry Argument of a Line Charge

I am been trying to make sense of my professor's lecture notes on where he talks about line charges; in general, I am lost when it comes to the symmetry argument in the case that $$E_\phi=0$$ on an infinitely long line charge that is constant for $$\lambda$$, which could or could not be counterclockwise. At the same time, he talks about using the same symmetry argument which he claims that $$B_\phi=0$$ on an infinitely long wire with a constant current $$I$$ does not apply to the claim prior.

I know that $$I$$ and $$B_\phi$$ are not zero, but I am unsure how that would relate.