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How to approach this problem? (electrostatics, capacitors)

Physics Asked by Wolfcho on February 21, 2021

The problem:

A flat capacitor is made of two strips of width $a$ and length $l$. The distance between them is $d$. Determine the capacitance of that capacitor if you roll it into a multi-turn roll of radius $R>>d$.

My opinion: If you make the above-stated roll, then as I see I get some kind of a spiral. If so, then it’s usefull to use polar coordinates to get the equation for the two sides of the capacitor:

The outer side:$$ side1 = {θ+d} $$
The inner side:
$$ side2 = {θ} $$

But in result I can’t think of a way to continue the solution.

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