## Electric Flux on a Cylindrical Gauss Surface

1. The problem statement, all variables and given/known data

A cylinder of length L and radius R is centered on the z-axis in a region where there is a uniform electric field of E i. Determine the flux for the fourth of the cylindrical surface where x > 0 and y > 0.

2. Relevant equations

$$\phi = \int E dS$$

3. The attempt at a solution

I believe I have the sketch drawn as the problem states.

If you were to take the entire surface, you'd see:

$$\phi = \int E dS$$
$$\phi = E \int dS$$
$$\phi = E (2\pi RL)$$
$$\phi = 2E\pi RL$$

I'm confused though. Wouldn't a Guassian surface, such as the cylinder, ultimately have zero flux in the above Electric Field?

I don't know how to progress using Gauss's Law to cut this into a fourth. I don't see how I can use symmetry to develop a method to use the law.
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 Recognitions: Homework Help Science Advisor Find the flux through the L by 2*r rectangle that goes through the axis of cylinder and is perpendicular to the E field. The incoming and outgoing flux through the cylinder are both equal to that, right? Sure, that makes zero total flux. But the flux through the two quarter cylinders are both equal.
 So you're saying I should take a Gaussian rectangle and do this to it: $$\phi = \int \vec{E} \cdot d\vec{S}$$ $$\phi = E A cos \theta$$ $$\phi = E (2RL)(1)$$ $$\phi = 2ERL$$ This gives us the flux through the rectangle as 2ERL. The correct answer to the problem is ERL (1/4th of the cylinder). However, I do not follow the reasoning why I took this Gaussian surface or why it's useful in finding the cylinder's flux.

Recognitions:
Homework Help