Capacitor of different plate dimensions

[arka210]

1. Is it possible to calculate the capacitance of a system where the top plate has the dimension d1 and the bottom plate has a dimension d2 and d1<<d2. Now, the difference between the plates are t. Is it possible to calculate the capacitance of this system where the dielectric is oil?

2. In one of the thread here namely "Capacitance of two different circular plates" (last post June, 08), I got some basic idea from this thread but they consider air as dielectric, while in my case dielectric is oil. Also I need a mathematical computation guideline for this capacitor system

The Attempt at a Solution

 

[graphene]

You can assume that not all of the bigger plate contributes. The part of the bottom (bigger) plate directly below the top plate would only contribute. So, it is just like a capacitor of plates with dimensions as that of the smaller plate.

This comes from the assumption that that field due to the capacitor plates are like those due to an infinite plane. If not, then it'd be messy.

What happens to the field in a dielectric?

 

[arka210]

Thanks graphene for your reply.

From one of the thread here I got an idea, quite similar to what you said >> "one can start with the smaller area to get an initial number, and then add in some more to account for the field lines that go from the outer part of the larger plate to the fringe / edge / backside of the smaller plate. It might be easiest to do it numerically". Question is whether this idea is applicable or not if the dielectric is oil and not air?

 

[aim1732]

Only difference it would make is that dielectric constant K would change from 1 to a greater number.

 

[arka210]

As I mentioned before "one can start with the smaller area to get an initial number, and then add in some more to account for the field lines that go from the outer part of the larger plate to the fringe / edge / backside of the smaller plate. It might be easiest to do it numerically".
Now adding some more field lines is possible.
The question is how can I justify it? Is there any papers/publications or theory from which I can justify this computation?