Capacitance of two different circular plates

[sander]

Does anyone know how to calculate the capacitance of two circular plates having different dimensions?

Say the top capacitor plate has a diameter d1 and the bottom capacitor plate has a larger diameter d2 and air is in between the bottom and top plate. So, it is not a standard parallel plate capacitor, but there is a difference in plate sizes!

How to calculate this capacitance in this case?

 

[tonyh]

Does anyone know how to calculate the capacitance of two circular plates having different dimensions?

Say the top capacitor plate has a diameter d1 and the bottom capacitor plate has a larger diameter d2 and air is in between the bottom and top plate. So, it is not a standard parallel plate capacitor, but there is a difference in plate sizes! How to calculate this capacitance in this case?

As per usual, but use the common (smaller) area for A.

 

[sander]

Thanks for your reply tonyh, but I doubt if I can simply use the smaller area. On the contrary, in some scientific papers they use the larger area instead of the smaller. But I can't find a proper reason for choosing any of the two. Do you have any reference theory to support your suggestion?

 

[tonyh]

Thanks for your reply tonyh, but I doubt if I can simply use the smaller area. On the contrary, in some scientific papers they use the larger area instead of the smaller. But I can't find a proper reason for choosing any of the two. Do you have any reference theory to support your suggestion?

No I don't - sorry. I was going by an example in one of my physics textbooks, re an old-fashioned style variable cap where you vary the capacitance by varying the area of overlap. And it says that the capacitance is proportional to the area of overlap.

 

[berkeman]

Does anyone know how to calculate the capacitance of two circular plates having different dimensions?

Say the top capacitor plate has a diameter d1 and the bottom capacitor plate has a larger diameter d2 and air is in between the bottom and top plate. So, it is not a standard parallel plate capacitor, but there is a difference in plate sizes!

How to calculate this capacitance in this case?

That's not an easy calculation. You can start with the smaller diameter 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... Is this for a standard E&M class?

 

[pam]

If d1<d2 and the distance between (t) is << d1, then it is appropriate to use the smaller area.
The part of the larger plate beyond d1, will have no charge on it.
If t is large, it gets quite complicated.

 

[sander]

No, it is not for a standard E&M class, but for a scientific project.

The problem is that I would like to determine the area of the bottom capacitor plate once the capacitance is measured. So, in fact, I know the area of the top capacitor plate, the distance (t) of the air gap and the total capacitance. But I don't know how to determine from this the area on the bottom capacitor plate. Pam: the distance (t) is very large compared to the d1 and d2.

 

[berkeman]

No, it is not for a standard E&M class, but for a scientific project.

The problem is that I would like to determine the area of the bottom capacitor plate once the capacitance is measured. So, in fact, I know the area of the top capacitor plate, the distance (t) of the air gap and the total capacitance. But I don't know how to determine from this the area on the bottom capacitor plate. Pam: the distance (t) is very large compared to the d1 and d2.

If the separation t is >> d, then parallel plate capacitor formulas would not apply. It also sounds like it would be difficult to make an accurate measurement of this capacitance, depending on the noise environment. Can you say what you are trying to do exactly? There may be another way to accomplish the task.

 

[Meir Achuz]

It t is large, the capacitance will be very small and would be affected by things like distance to the wall or to you. For large t, a reasonable approximation would be to consider each plate as a uniformly charged disk with charges +Q and -Q. Then you can calculate the potential on the axis, and use C=Q/V. It's not as hard as I thought at first.