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

In summary, Laplace's equation is used to solve boundary-value problems. These problems involve determining the value of a function at an arbitrary point in space. The equation can be used to calculate the concentration of external fields, and it is a useful tool for solving problems in electromagnetism.
  • #1
Mehrdad
4
0
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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  • #2
Hello!1
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Thanks for guide But:
would you help me and give me some examples , Please...
 

1. What is Laplace's Equation in 3D space?

Laplace's Equation in 3D space is a partial differential equation that describes the behavior of a scalar field in three-dimensional space. It is used in many areas of science, including physics, engineering, and mathematics.

2. What is a boundary value problem (BVP)?

A boundary value problem (BVP) is a type of mathematical problem that involves finding a solution to a differential equation that satisfies certain prescribed conditions (known as boundary conditions) at the boundaries of the domain.

3. How are Laplace's Equation and BVP related?

Laplace's Equation can be used to model physical systems and solve BVPs. The boundary conditions in a BVP provide the necessary information to determine a unique solution to Laplace's Equation in 3D space.

4. Can you provide an example of a BVP using Laplace's Equation in 3D space?

One example of a BVP using Laplace's Equation in 3D space is the electrostatics problem of finding the electric potential inside and outside a charged conducting sphere. The boundary conditions in this problem would be the given charge distribution and the potential at the surface of the sphere.

5. What are the applications of Laplace's Equation in 3D space BVP?

Laplace's Equation in 3D space BVP has many applications in physics, engineering, and mathematics. It is used to model and solve problems related to heat transfer, fluid flow, electrostatics, and many other physical phenomena.

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