(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let's say you have a solid cylinder. It is nonconducting. It is long enough such that the contributions from the ends are negligible. It has a non-uniform volume charge density of Ar^2, where A is some positive constant. Then you are asked to find the electric field at different radii, respectively.

This is a problem that I was given as homework. What confuses me is that the authors assume that the Flux, F, = E(Surface Area of curved area). That is, F = E2[itex]\pi[/itex]RH, where H is the height of the cylinder. Typically, this I have no problems with this; I understand what is going on (typically). However, in this case I see nothing in the problem that warrants the assumption that the flux can be rewritten as F=Ecos(0)2[itex]\pi[/itex]RH. Am I missing something here? Couldn't the Electric field be written as <x,y,z>. In which case, the the angle between the Electric field and the normal vector pointing out from the surface would NOT be 0. Thus, making the assumption false.

Is it the case that anytime you have a gaussian surface that is a cylinder, the Electric field will always be parallel to any normal vector to the surface. Or is there something in the problem that warrants the assumption that this is true?

Btw, the problem only contains the following information: that is a cylinder, it is really long, it has a non-uniform charge density = Ar^2. A = 2.5[itex]\mu[/itex] C/m^5, the radius of the cylinder is .04 m. And we are to find the electric field at r = 3 cm and r = 5 cm.

Given that I make the assumption that the angle between E (vector, not magnitude) and a normal vector to the (curved) surface is 0, I can solve the problem. However, I can't find any reason to make the assumption.

Any explanation would be great.

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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# Cylinder, Electric flux

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