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I'm confused as to how this expression E= (δ/

*εo*) can't be used to calculate the electric field of a perfectly flat part of a surface even farther from just above the surface.If you just extend the same cylindrical Gaussian surface used for this proof, wouldn't the field stay the same no matter how far out you go? The charge enclosed on the surface of the conductor wouldn't change and neither would the area of the circular end of the cylinder sticking out of the conductor since it sticks out of a flat surface. Obviously this simply cannot be so as the field should grow weaker with distance from its charged source, so I wonder what about this proof I'm misunderstanding. On a related note, what about the derivation for E=(δ/2*εo*) for an infinitely charged plane takes into account its infinite size, as it seems to me that it could just as easily be used to calculate the electric field for a finite sheet of charge?
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