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say we have an infinite plane slab of thickness 2d, with uniform charge density ρ. Find the function of the electric field with regards to y where y=0 is at the center of the slab.

Then

[itex] Q/ε = \oint E dA [/itex]

so I draw my cylinder inside of the plane. I imagine 1 face at y=0 and 1 face at y < d. then,

[itex] Q = (ρ A (y))/ ε = E * 2A [/itex]

where A is the area of the face of our cylinder, and we can ignore the sides of the cylinder since the flux is parallel there.

However in my book they draw the second face coming out of the cylinder, and the final answer is just [itex] ρy/ε.[/itex]

I for the life of me don't understand why we differ by a factor of two.

Thank you,

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