Use Gauss's law to find the electric field caused by a thin, flat, infinite sheet with a uniform positive surface charge density σ.
φ(flux) = ∫E*dA = qencl / ε0
The Attempt at a Solution
I set up a diagram like this: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html#c1
1) I'm sorry if this is a really vague question but I don't get why the cylinder is smaller than the sheet? I thought the cylinder would have to enclose the sheet? If we don't enclose all the charge of the plane, how can we use Gauss's Law?
then EA = qencl / ε0, because I assumed E and A are constants in this situation.
A = 2πrL, where L is the length of the gaussian cylinder.
then E = qencl / (ε0 * A)
E = qencl / ε02πrL
which is so wrong..
I read the answer in the book but these are what makes no sense to me:
1) The flux though the cylindrical part of the cylinder is zero because E * n = 0 everywhere.
2) The flux through each flat end of the surface is +EA because E * n = E everyone, so the total flux through both ends is +2EA.
If I assume these two things are true I understand what they do after which is
2EA = σA / ε0
E = σ/2ε0
Please help on how I can understand what the book is telling me in 1) and 2) and also how do they arrive at the diagram that they do?