Discrepancies with Coulombs law?

1. The problem statement, all variables and given/known data

E obeys Coulombs law, i.e. E is proportional to 1/r^2. However, between a parallel plate, E = constant and in coaxial cylinders E is proportional to 1/r. What is the explanation for these discrepancies?
2. Relevant equations

3. The attempt at a solution

I think that Coulomb’s law is only for point charges. Coulomb’s Law does not state that E is proportional to 1/r². It states that E due to a stationary point charge is proportional to 1/r². Parallel electrodes and concentric electrodes aren’t stationary point charges, so there’s no reason to expect the field they produce to be proportional to 1/r².
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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