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There is a slick way to solve this problem (and a host of similar....
problems). It is both quantitative and intuitive.
The trick is to convert this seemingly electrostatic problem into an
electrodynamic problem. Near the end of the calculation we let the
frequency tend to zero and recover the electrostatic result.
1) For simplicity, replace your circular tube with one that has a
rectangular cross section.
Cheers --- jsdWow! Now THAT'S what I call a physical intuition.