Why is the flux on top and bottom of a cylinder ignored in Gauss's law?

AI Thread Summary
In the discussion on Gauss's law applied to a cylinder, the flux through the top and bottom surfaces is considered zero because the electric field is perpendicular to these surfaces, resulting in no contribution to the total flux. The focus is on the cylindrical side surface where the electric field is uniform and directed outward. The conversation humorously touches on the application of Gauss's law to various shapes, emphasizing that the scenario dictates the electric field behavior. It is noted that for a long wire, the electric field at the ends cancels out, justifying the zero flux assumption. Overall, the treatment of flux in Gauss's law varies based on the specific geometry and charge distribution involved.
Acuben
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Homework Statement



(first of all, let me know if I am wrong in any parts)
gauss's law can be used on cylinder.
Why is it that flux on top and flux on bottom of the cylinder, with area pi*r^2 ignored? (aka, equal to 0)
such that
Flux= Integral(E*da)=E2(pi)rl=q/(Eo)
where (Eo) is permitivity of/in vacuum.

Homework Equations



Cylinder
Flux= Integral(E*da)=E2(pi)rl=q/(Eo)
Sphere
Flux= Integral(E*da)=E2(pi)r^2=q/(Eo)

The Attempt at a Solution

 
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What are you uses gauss' law ON? a wire? a uniform sheet? constant charge density? a banana?
 
Mmm, gaussian banana.
 
zhermes said:
What are you uses gauss' law ON? a wire? a uniform sheet? constant charge density? a banana?

nothing in particular. I meant making an gaussian cylinder in general did not define what I am using it on.
Although if it's a long wire, I suppose there is no Electric field towards top and bottom and it cancels out.
 
in that case the answer to your question is: 'it depends on the situation.'
 
Mindscrape said:
Mmm, gaussian banana.

That can only be solved using a bananal coordinate system.
 
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