Capacitance between two coplanar electrodes

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Homework Statement



I have two coplanar electrodes (180 deg between them) and one of them is under voltage causing circular electric field between them. The target is to calculate the capacitance.


Homework Equations


Using the capacitance equation C = [tex]\frac{\epsilon_{0}A}{l}[/tex]
I say that A = bdx and l = [tex]\pi[/tex]r
b - is out of plane length of the electrodes

The Attempt at a Solution


I'm integrating the equation from R1 to R2 (coordinates of electrode on x axis)
but I have to substitute dx with something else - x = rCos[tex]\theta[/tex] so that
dx = cos([tex]\theta[/tex])dr

so the solution is C= [tex]\frac{\epsilon_{0}bCos\theta}{\pi}ln\left(\frac{R2}{R1}\right)[/tex]

Am I doing it rigth?
 

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