Why Does Gauss's Law Use Cylinder Circumference Instead of Area?

AI Thread Summary
Gauss's Law applies to cylindrical symmetry, where the electric flux is calculated using the electric field and the surface area of the cylinder. The confusion arises from the use of the cylinder's circumference instead of its total surface area. The relevant area for calculating electric flux is the curved surface area, which is determined by multiplying the circumference by the cylinder's length. This is because electric field lines do not pass through the cylinder's ends, making the ends irrelevant for this calculation. Understanding this concept clarifies why the circumference is used in the context of Gauss's Law for cylindrical shapes.
CollegeStudent
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Homework Statement



So I was looking at this site reading up again on Gauss's Law and was a tad confused

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html

1st thing on the page...

Homework Equations


The Attempt at a Solution



It states that the electric flux will just be the Electric field times the area of the cylinder...

However in the calculation, the circumference of the cylinder is used...why is that?
 
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CollegeStudent said:
However in the calculation, the circumference of the cylinder is used...why is that?
The circumference times the length L gives the surface area.
 
Oh okay! I was taking into account the full area but since the Electric field lines will never cross through the 2 ends of the cylinder the area needed will just be the circumference times the length..

Thank you Doc Al!
 
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