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Q & A: asymmetrical parallel plate capacitor

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Most recent answer: 07/17/2013
Q:
If we take a parallel plate capacitor containing two plates of areas A1 and A2 which area i want to find capacitance.why?
- Kadiri praneeth (age 16)
A:

That's an interesting question. Let's stick to the simple case where the distance between the plates is a lot smaller than the size of even the smaller plate. Now let's think about an even further simplification: let one of the plates be infinite. We can exactly reproduce the electric field between the plates by ignoring the infinite plate and putting its charge on another small plate at twice the distance. Of course this new arrangement has similar fields on both sides of the middle plane, so it has twice the electrostatic energy of the original capacitor, for the same charge. That means it has half the capacitance. Since the spacing is small, that means that a capacitor with two plates the size of the small plate, at the same distance as the original plates, has the same capacitance. It seems as if only the size of the small plate matters.

This conclusion cannot be exactly right. Adding to either one of the plates must increase the capacitance at least a bit. If you have two plates very slightly different in area, I bet the capacitance depends on the average. However, once one of the plates extends outside the range of the other by much more than the separation of the plates, very little field will extend out that far. So if you start to make one of the plates bigger than the other, the capacitance will grow a bit at first, then level off. In the small-separation approximation, it's basically just the smaller plate that matters.

Mike W.


(published on 07/17/2013)

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