Boundary Potential Problem- parallel alternating potential

In summary, a Boundary Potential Problem is a mathematical problem used in physics and engineering to find the potential function at the boundaries of a given region. A parallel alternating potential is a type of boundary potential problem where the potential function varies periodically between two parallel planes. To solve this problem, mathematical techniques such as separation of variables or Fourier series are used. This type of problem has many practical applications, such as modeling the behavior of parallel plate capacitors and studying electric and magnetic fields. However, it has limitations, such as assuming perfectly parallel boundaries and becoming more complex for complicated systems.
  • #1
ebru
3
0
Homework Statement
Hello,
I have a question about the potential. I think the potential shoul be something like below. In that way periodic behavior work perfectly. But I don't know how to add the x variable to the equation.
Relevant Equations
So how can I find potential?
1571844917625.png


1571845223091.png
 

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  • #2
Well this amounts to solving a Laplace equation for potential, right?
$$\Delta \phi = -\frac{\rho}{\epsilon} = 0$$
I would solve this 2D Laplace equation for a rectangle defined by ##0<x<a## and ##0<y<b##. Then once you have the potential inside that rectangle, you would periodically extend it over ##y##. I assume you're familiar with this equation since you're asking this kind of a question, if you're not, I can give you some introduction to it in the next post.
 

1. What is a Boundary Potential Problem?

A boundary potential problem is a type of mathematical problem that involves finding the potential function in a given region, subject to certain boundary conditions. It is commonly used in physics and engineering to model the behavior of electric fields, heat flow, and other systems.

2. What is a parallel alternating potential?

A parallel alternating potential is a type of boundary potential problem where the potential function alternates between two different values along two parallel lines. This creates a series of alternating regions with different potential values.

3. How is a boundary potential problem solved?

Boundary potential problems are typically solved using mathematical methods such as separation of variables, the method of images, or complex analysis. These methods involve breaking down the problem into simpler equations and solving for the potential function in each region.

4. What are the applications of a boundary potential problem?

Boundary potential problems have many practical applications in physics and engineering. They can be used to model the behavior of electric fields in capacitors, heat flow in insulated materials, and fluid flow in pipes.

5. What are the limitations of a boundary potential problem?

Boundary potential problems are limited in their ability to accurately model real-world systems. They often make simplifying assumptions and may not take into account factors such as non-uniformity of materials or external influences. Additionally, they may only provide an approximate solution, rather than an exact one.

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