1. The problem statement, all variables and given/known data Problem statement: An infinitely long, straight line has a uniform charge distribution of ρ C/m. Use Gauss' law to find the electric field at a point r m away from it. Solution: Consider a cylindrical volume of height ℓ with circular cross sectional area of radius r, which has the line as its axis. The volume contains a total charge of Q = ρℓ. By symmetry, the E field is radial in direction and has the same magnitude on the surface of the cylinder. The total flux through the surface is Ψ = ϵE × ℓ × πr^2. By Gauss' law, Ψ = Q from which E = ρ/(πϵr^2). 2. Relevant equations Gauss' Law. Cylinder. 3. The attempt at a solution I'm trying to understand the given solution. Is Q = ρℓ instead of Q = ρV true, because the charge is distributed along the real-world line instead of the imaginary cylinder? And, what about Gauss' Law indicates that Ψ = Q? Also, I keep seeing the capital letter phi, Φ, in the context of Gauss' Law. Is Φ from what I see on-line the same thing as the Ψ I see in my book? Lastly, how was the total flux found to be Ψ = ϵE × ℓ × πr^2? For what it's worth, given Ψ = Q, Q = ρℓ and Ψ = ϵE × ℓ × πr^2, I do know how to get E = ρ/(πϵr^2). Any input would be GREATLY appreciated!