Example Questions of Laplace's Equation in 3D Space BVP

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SUMMARY

This discussion centers on the need for example questions related to Laplace's equation in boundary-value problems (BVP) in 3D space. The user, a Power Electric Engineering student, requests at least 20 examples to prepare for an upcoming electromagnetism exam. Participants emphasize the importance of demonstrating prior understanding and suggest practical applications of Laplace's equation, such as calculating the concentration of B-field lines in various geometries, including cubes and toroids.

PREREQUISITES
  • Understanding of Laplace's equation and its applications in boundary-value problems.
  • Familiarity with electromagnetism principles, particularly in 3D contexts.
  • Basic knowledge of numerical methods for solving differential equations.
  • Experience with geometric shapes and their properties in relation to magnetic fields.
NEXT STEPS
  • Research practical applications of Laplace's equation in electromagnetism.
  • Explore numerical methods for solving boundary-value problems in 3D space.
  • Study the effects of different geometries on magnetic field concentration.
  • Find or create a repository of example problems related to Laplace's equation in BVP.
USEFUL FOR

This discussion is beneficial for Power Electric Engineering students, educators in electromagnetism, and anyone involved in solving boundary-value problems using Laplace's equation in three-dimensional contexts.

Mehrdad
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Need To Example Questions Of "laplace's equation in Boundary-value Problem"in 3DSpace

Please Help Me : Need To Example Questions Of "laplace's equation in Boundary-value Problem"in 3D Space.

Can Anyone Give Me a File That Contains This Type Of Questions?

I Need At least 20 Examples.

Please Help.

Thanks.
 
Last edited:
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Hello!1
 
Welcome to the PF, Mehrdad. In order for us to help you, you need to show us some of your own work and understanding of the material behind the problem. What can you tell us about using Laplace's equation in boundary-value problems? When is it used, and what are you solving for?

I've used it for at least one pretty cool application, but I'm not inclined to post it unless I see some work from you. We do not just give out solutions to homework problems here on the PF.
 
Oh Thank God.
I Am A ((PowerElectric Engineering)) university student In Iran and I have An Important Exam Of Electromagnetism In Few Days Later.
I Must Practice And My Problem Is That I Have Just Three Example Of That Type Of Questions.I`m afraid And I Need This Type Of Examples To Practice much More.

Please Help Me And Give Me The Examples.

Thanks.
 
Well, the problem that I had to figure out was how much a high-mu toroidal transformer concentrated external B-field lines. This was needed in order to quantify the effects of external B-field noise on the pickup voltage in the transformer.

So I don't know if it helps your practice or not, but you can calculate how much the B-field lines are concentrated by various 3-D shapes of high mu material. Start with a cube, and then change the aspect ratio of the cube into a long skinny box, or a short wide box, etc. The numbers you get are pretty interesting. I solved my 3-D toroid problem numerically on a PC, but for simpler geometries like a cylinder or box, you might be able to solve them by hand.
 
Thanks for guide But:
would you help me and give me some examples , Please...
 

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