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Homework Statement
Find the field at A.
Homework Equations
##\oint E\cdot dA = Q_{enclosed}/\epsilon_0##
The Attempt at a Solution
My first intuition was to do a Gaussian cylinder from A to the middle of the bottom plate. My logic is that the field inside the bottom plate is 0, so I'd have (from Gauss' Law) ##E(\pi r^2) = (10  2  1)\sigma \pi r^2/\epsilon_0##, so ##E = 7\sigma / \epsilon_0##. However, the correct answer is with a coefficient of 1.5, which I get if I do a Gaussian cylinder from A to D.
This also got me thinking: if I do a Gaussian cylinder from middle of the top plate to the middle of the bottom plate, my understanding is that field is 0 at the top and bottom of my Gaussian surface. Yet, ##E(2\pi r^2) = (10  1  1)\sigma \pi r^2/ \epsilon_0## and this suggests to me that field is nonzero inside the plates. What is wrong with my understanding here? Does this suggest that field is nonzero inside the plates?
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