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Suppose you have a line of charge with a uniform linear charge density of λ=15μC/m. What is the electric flux through a cylinder with radius R=0.5 m, and length l=3 m that is placed so that its axis is aligned with the line of charge? Feel free to use the electric field due to an infinite uniform line of charge: →E=λ2πrϵ0ˆr (where ˆr points away from line, and r is the distance from the line).
Φe=∫→E∙d→A
→E=λ2πrϵ0ˆr
There are a few approximations and assumptions we should make in order to simplify our model.