Capacitance Across Not-So-Parallel Plates

[^eMpTy^]

I'm trying to calculate the capacitance across a couple of parallel plates but, for fun, one of the plates looks like a stair step. So it has 2 sections facing one normal parallel plate at different distances.

I see two possibilities here, one being that I can simply treat the two sections as two sets of parallel plate capacitors and apply the appropriate formula using two different distances for each section.

However that leaves the perpendicular part of the stairstep unaccounted for. So my second thought was that I would have to do an integral across that part of the surface from one distance to the other. But since there is zero exposed surface area that is parallel to the regular straight plate, that doesn't quite make sense to me either.

If that all made sense to you...can you kick me in the right direction?

 

[mukundpa]

!Yas

Actually the angle is very small and therefore the unexposed area can be neglected.

You have to integrate.

I think this in "Concepts of physics" by Resnik and Halliday. I have solved it earlier.

 

[lightgrav]

If the step has "really small Area"
(compared to the total plate Area),
just treat it like 2 capacitors.

alternate way of deciding:
If you know how to find the E-field near
a conductor with an inside corner like that,
accounting for the varying charge density,
then go for it.