Electric Field between concentric cylinders

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I wanted the electric field between concentric cylinders, and got anexpression using Gauss' Law that considers only charge enclosed. Thus, there was no influence due to the outer cylinder.
But, if we consider the limiting case of the inner cylinder having very large curvature and the outer cylinder not too far off from it..i.e a is very large and b is just larger than a.
I assume that then the electric field between the cylinders can be considered as a flat plate analogy, which gives some other answer of the field between(for flat plate analogy, the outer cylinder also supplies electric field but it had no influence watsoever when we considered the normal cases)...Please help. I cant figure out what's wrong.
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And suppose now, I consider both the cylinders to be dielectrics. Does that affect the analysis? Will the Gauss' Law still be applicable? Will the field inside an infinitely long uniformly charged cylinder still be zero, and have no affect on the electric field between the Dielectrics??

• Electric Field between concentric cylinders - ,

Gauss Law applies, no matter if the inner surface is curved, or flat. It is the charge enclosed in the gaussian volume that affects the field through the gaussian surface.