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I am trying to solve this problem. I would like to be able to solve for the capacitance between two parralel plates of different areas.

First I tried thinking of them as concentric cylindrical shells but twisting them to do this is not the same thing I realized because the distance between the two plates would be huge, where if they are left straight it is a very small differnce

So I am thinking of doing something similar to say Griffiths problem 3.9, but with plates instead of line charge. And i am stuck because I can tell already this is gonna be hard math. If I assume one plate is really small compared to the other or if one is say infintie will this help solving the problem?

Any help would be appreciated, I think if I could figure the E field out for this case I could then find the capacitance with out much hassle.

One plane is E=(surface charge)/(2*epsilon not) ...infinite

the other should be E=(surface charge)(ab)/(4*pi*epsilon not*r^2), where ab is the area of the plate

if the top plate is not infintie then I could use the bottom formula twice but with a2b2 right?

Then To find the efield in between the two plates I would just have to use superpostion to add the fields right?

Integrate then from bottom plate to top plate for voltage, and have q divided by that, this should be my capacitence ehh?

Thanks

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# Parallel Plates Different areas

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