# Non ideal parallel plates (really quick question)

In summary, the conversation discusses the use of numerical techniques to solve a simple parallel plates capacitor problem. It is mentioned that there is no closed form solution for Laplace's equation when dealing with fringing effects, leading to the use of numerical techniques. However, in an idealized model, closed form solutions can be obtained for some fringing effects. It is noted that conformal mapping can be used in some cases, but it may not be able to handle the fringing effects in a parallel plates capacitor. The conversation concludes with an agreement to continue with the numerical work for the report.
I'm writing a report about using numerical techniques to solve a simple parallel plates capacitor problem.

Would it be proper to say that there is no closed form solution to Lapalces equation when dealing with fringing effects? Isn't this the reason why we use numerical techniques to solve the problem?

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well in an idealized model, you can get closed form solutions for some fringing effects. However, i think it would be fair to say that you can't analytically solve for the fringing effects of any physical capacitor since there would be imperfections in the manufacturing process that would make it impractical, if not impossible, to get an exact solution for the potential even considering only classical electrodynamics.

I'm writing a report about using numerical techniques to solve a simple parallel plates capacitor problem.

Would it be proper to say that there is no closed form solution to Lapalces equation when dealing with fringing effects? Isn't this the reason why we use numerical techniques to solve the problem?
Conformal mapping can be used. I think that Panofsky and Phillips does it.

Meir Achuz said:
Conformal mapping can be used. I think that Panofsky and Phillips does it.

So I really shouldn't say that there is no closed form solution. This is just for an introductory emag engineering class, so I don't want to say things I don't know ;)

Sorry, I was too optomistic. I looked at P & P, and they do not do the fringing case. They just treat simpler cases. I donn't think conformal mapping can do the parallel plate frilnging. Get on with your numerical work.

Meir Achuz said:
Get on with your numerical work.

hehe, ok man.

Well I got that part done at least. Thanks for checking around.

## 1. What are non ideal parallel plates?

Non ideal parallel plates refer to a type of capacitor in which the parallel plates are not perfectly flat or evenly spaced apart. This can cause deviations from the expected behavior of an ideal parallel plate capacitor.

## 2. What factors can contribute to non ideal parallel plates?

Some factors that can contribute to non ideal parallel plates include surface roughness of the plates, uneven spacing between the plates, and the presence of dielectric materials between the plates.

## 3. How do non ideal parallel plates affect the capacitance of a capacitor?

The presence of non ideal parallel plates can decrease the capacitance of a capacitor compared to an ideal parallel plate capacitor. This is because the non ideal factors can disrupt the electric field and reduce the amount of charge that can be stored on the plates.

## 4. What are some techniques used to mitigate the effects of non ideal parallel plates?

Some techniques that can be used to mitigate the effects of non ideal parallel plates include using materials with higher dielectric constants, improving the flatness and spacing of the plates, and using shielding materials to reduce external interference.

## 5. How do non ideal parallel plates impact the overall performance of a circuit?

Non ideal parallel plates can impact the overall performance of a circuit by affecting the capacitance and thus the ability of the circuit to store and release charge. This can lead to changes in the frequency response and stability of the circuit.

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