Non-parallel plate capacitance

[ianmc7]

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.

 

[Meir Achuz]

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.