Capacitance of an asymmetrical parallel plate capacitor

In summary, the conversation discusses the difficulty in determining the capacitance between two parallel plates when one plate is larger than the other. The suggested approach is to use a numerical solution, taking into account edge effects. The example of a spherical capacitor is mentioned as a possible approach.
  • #1
nickexists
5
0
I've been looking all over and to my great surprise have not be able to find an answer to this question.

What is the capacitance between to parallel plates if one plate is larger than the other? For example, the capacitance between a 1" diameter plate and a 4" diameter plate.

Thanks.
 
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  • #2
The math gets quite tricky when you have situation like that. As a first approximation the capacitance would be nearly the same as for two identical plates (since most of the E-field lines will be perpendicular to the plates). However, if you want to take edge effects into account the calculation becomes tricky and in the "real world" you would probably have to solve this numerically.
 
  • #3
Thanks. I am actually interested in how this works out in the real world, do you know more specifically how I would go about solving this numerically?
 
  • #4
nickexists said:
What is the capacitance between to parallel plates if one plate is larger than the other? For example, the capacitance between a 1" diameter plate and a 4" diameter plate.
If the plates are close enough, the capacity will be very close to the capacitor of both plates plates being 1" dia
 
  • #5
A tricky integral over the volume of the E field... i don't know how one would establish outer bound.
See hyperphysics example of a spherical capacitor , for an approach...
 

1. What is capacitance?

Capacitance is a measure of the ability of an object to store an electrical charge. It is represented by the symbol C and is measured in farads (F).

2. How is capacitance calculated for an asymmetrical parallel plate capacitor?

The capacitance of an asymmetrical parallel plate capacitor can be calculated by dividing the permittivity of the material between the plates by the distance between the plates. The equation is C = εA/d, where ε is the permittivity, A is the area of the plates, and d is the distance between the plates.

3. What factors affect the capacitance of an asymmetrical parallel plate capacitor?

The capacitance of an asymmetrical parallel plate capacitor is affected by the permittivity of the material between the plates, the distance between the plates, and the area of the plates. Other factors such as the shape and arrangement of the plates may also have an impact.

4. How does the capacitance change if the distance between the plates is increased?

If the distance between the plates of an asymmetrical parallel plate capacitor is increased, the capacitance will decrease. This is because increasing the distance reduces the electric field between the plates, making it more difficult for the capacitor to store charge.

5. How does the capacitance change if the area of the plates is increased?

If the area of the plates of an asymmetrical parallel plate capacitor is increased, the capacitance will also increase. This is because a larger plate area means more space for the electric field to interact with, allowing the capacitor to store more charge.

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