Possible to create global potential from local distribution?

In summary, based on some figures, it is suggested to solve the spatial distribution of potential with Poisson equation.
  • #1
KFC
488
4
Hi all,
I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong potential of 3V in region of radius 10 grids at somewhere close to bottom-left corner, 5V in region of radius 15 girds at top-right corner, -1V in region of radius 15 grids in middle. With this distribution is it possible to create all contour potential lines based on those 3 strong regions such that the potential line are gradually change to span whole space (grids)?
 
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  • #3
Thanks. After reading that post, base on my understanding, it is suggested to solve the spatial distribution of potential with Poisson equation. The excel file found there use the average of neighboring points to estimate the value of the current point (that's the idea of solving Poisson equation?) But after reading something about Poisson equation, it is about potential distribution if the charge distribution is known. I wonder if it is the same case since here I know some spatial distribution of potential, I am looking for how the other part of potential in space look like.
 
  • #4
KFC said:
(that's the idea of solving Poisson equation?)
It is the discrete version of Poisson's equation in cartesian coordinates.
The charge distribution is known in every cell where you want to calculate the potential - it is zero (if it is not, the formulas need an additional term to account for that). You don't know the charge distribution at the electrodes, but there you know the potential.
 
  • #5
Oh, so you mean we actually use the Laplace equation instead of Poisson equation to solve the problem since we know the potential in space already? So just average each point with its neighbor will do the work, is that correct?
 
  • #6
If you have zero charge density where you want to calculate the potential (the usual case), both equations are identical.
You can fix the potential at some points, iterating the averages over neighbors will give an approximation for the potential elsewhere.
 
  • #7
got it. Thanks mfb.
 

Related to Possible to create global potential from local distribution?

1. Is it possible to create global potential from local distribution?

Yes, it is possible to create global potential from local distribution. Local distribution refers to the distribution of resources or ideas within a specific geographical area, while global potential refers to the potential impact or reach of these resources or ideas on a global scale. Through efficient and strategic distribution methods, local resources and ideas can be disseminated globally, creating a larger impact and potential for change.

2. How can local distribution lead to global potential?

Local distribution can lead to global potential through various means such as networking, collaboration, and technology. When local resources or ideas are shared and exchanged with other individuals or organizations on a global level, it can lead to the creation of new ideas, partnerships, and opportunities. Additionally, advancements in technology have made it easier to distribute and access resources globally, further increasing the potential for global impact.

3. What are the benefits of creating global potential from local distribution?

The benefits of creating global potential from local distribution are numerous. It allows for the sharing and exchange of ideas, resources, and knowledge on a global scale, leading to innovation, advancements, and solutions to global issues. It also promotes cultural understanding, cooperation, and collaboration among different communities and countries. Furthermore, it can help in the growth and development of local economies and industries.

4. Are there any challenges in creating global potential from local distribution?

Yes, there can be challenges in creating global potential from local distribution. One of the main challenges is ensuring equal access and distribution of resources and ideas globally. Language barriers, cultural differences, and varying levels of technology and infrastructure can also pose challenges. Furthermore, there may be resistance to change from certain individuals or groups who are not open to global collaboration or exchange.

5. How can we overcome the challenges in creating global potential from local distribution?

To overcome the challenges in creating global potential from local distribution, it is important to prioritize inclusivity and diversity in distribution methods. This can involve translating resources into different languages, considering cultural sensitivities, and providing access to technology in underprivileged areas. Collaborative efforts and partnerships between different communities and organizations can also help in overcoming challenges and promoting global potential from local distribution.

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