Non-parallel plate capacitance

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Calculating the capacitance of a non-parallel plate capacitor with varying separation requires integrating the voltage over the distance between the plates. The distance is defined as x=d+ay/L, where a is a small deviation from the average separation d. The goal is to prove that the capacitance C can be expressed as C= epsilon_not A/d (1+a^2/3d^2). The approach involves integrating V/(d+ay/L) from y=-L/2 to +L/2 and expanding the logarithm to simplify the expression. This method provides a pathway to derive the desired capacitance formula.
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Im having trouble calculating the capacitance of a non-parallel plate capacitor where separation at one edge is d-a and the other it is d+a, assuming a<<d. I'm supposed to prove that C= epsilon_not A/d (1+a^2/3d^2). Thanks for the help.
 
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The equations for the distance between the plates is x=d+ay/L.
The surface charge ~V/x.
Integrate V/(d+ay/L) from y=-L/2 to +L/2.
Expand the logarithm.
 
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