Capacitor Edge Effect: Math Analysis

In summary, the conversation revolves around the search for a mathematical analysis of the edge effect of a parallel plate capacitor. The reference given is A. Sommerfeld's Lectures on Theoretical Physics vol. III, which is highly recommended for learning about classical physics. The relevant problem is II.4 and has well-worked out solutions. However, there is no legal link available for the book and the person is unable to find it in their library. They request for a picture of the worked out problem.
  • #1
Anastasis Pk
4
0
Hello, I have been searching for a mathematical analysis regarding the edge effect of a parallel plate capacitor. Could anyone help?
 
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  • #2
There's a treatment of the semi-infinite case in

A. Sommerfeld, Lectures on Theoretical Physics vol. III.
 
  • #3
Thank you for your response. I can't find that reference in these lectures. Can you help?
 
  • #4
Well this shows that you didn't consider the really excellent problem set at the end of these books (BTW I think they are masterpieces; concerning classical physics they are among the best sources to learn from, although sometimes they are a bit outdated, e.g., in the use of the "ict convention" for special relativity or in the avoidance of the Dirac ##\delta## distribution (although it was in fact Sommerfeld who invented the concept some decades before Dirac). Anyway, you find the treatment of the edge effect as problem II.4 as an elegant application of conformal mappings for 2D potential theory). Note that all problems have well-worked out solutions!
 
  • #5
Can I please get the link wherein that book/ that question can be found ??
 
  • #6
There is no legal link to that book. It's

A. Sommerfeld, Lectures on theoretical physics vol. 3, electrodynamics, Academic Press 1952
 
  • #7
I cannot find that book, anyhow anyway in my library
Can u please drop in here, the picture of that worked out problem I will be immensely grateful to u for that
Please !
 

1. What is the capacitor edge effect?

The capacitor edge effect refers to the phenomenon where the electric field at the edges of a capacitor is stronger than at the center, resulting in a higher capacitance value compared to the theoretical value. This effect is caused by the fringing electric field lines that extend beyond the plates of the capacitor.

2. How does the capacitor edge effect affect circuit performance?

The capacitor edge effect can lead to inaccuracies in circuit calculations and measurements, as the actual capacitance value can be higher than expected. This can result in timing errors and other performance issues in electronic circuits. Therefore, it is important to take this effect into consideration when designing and analyzing circuits.

3. Can the capacitor edge effect be minimized or eliminated?

While the capacitor edge effect cannot be completely eliminated, it can be minimized by using specific capacitor designs and placement techniques. For example, using capacitors with smaller plate separation and larger plate area can reduce the impact of the edge effect. Additionally, placing the capacitor closer to the ground plane can also help mitigate the effect.

4. How is the capacitor edge effect mathematically analyzed?

The capacitor edge effect can be mathematically analyzed by using the edge effect factor (EEF), which is a correction factor applied to the theoretical capacitance value to account for the fringing electric field. This factor can be calculated using various mathematical models, such as the parallel plate model or the finite element analysis method.

5. Does the capacitor edge effect only occur in parallel plate capacitors?

No, the capacitor edge effect can occur in any type of capacitor with parallel plates, including ceramic, film, and electrolytic capacitors. However, the magnitude of the effect may vary depending on the specific type and design of the capacitor. It is important to consider the edge effect in all types of capacitors to ensure accurate circuit analysis and design.

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