Potential inside a rectangular pipe

In summary, the independence of potential inside an infinite rectangular pipe along the z axis has to do with symmetry and the uniqueness theorem. The potential is not affected by changes in the z coordinate due to the uniformity of the structure. This topic was discussed in the PF schoolwork forums.
  • #1
better
1
0
TL;DR Summary: Independence of potential( inside a rectangular pipe running along z axis)from z coordinate

Consider the following diagram

Screenshot_2023-06-08-15-34-01-36_e2d5b3f32b79de1d45acd1fad96fbb0f.jpg

It is an infinite rectangular pipe running along z axis.I know that the potential inside the pipe is independent of z coordinate, but I cannot seem to convince myself of it.My guess is that it has to do something with uniqueness theorem.
 
Physics news on Phys.org
  • #2
Welcome to PF. I've moved your thread to the schoolwork forums.

What equations would apply to this problem?
 
  • #3
better said:
My guess is that it has to do something with uniqueness theorem.
Symmetry, I'd have said. Everywhere along the axis looks like everywhere else.
 

FAQ: Potential inside a rectangular pipe

What is the potential inside a rectangular pipe?

The potential inside a rectangular pipe typically refers to the electric potential or the solution to Laplace's equation under specific boundary conditions, such as the potential being zero on the walls of the pipe.

How do you solve for the potential inside a rectangular pipe?

To solve for the potential inside a rectangular pipe, you generally use separation of variables to solve Laplace's equation. This involves expressing the potential as a product of functions, each depending on a single coordinate, and applying the boundary conditions to determine the constants.

What boundary conditions are used for a rectangular pipe?

The boundary conditions for a rectangular pipe typically specify the potential on the walls of the pipe. Commonly, the potential is set to zero on all walls, but other boundary conditions can be applied depending on the specific problem.

What are the eigenfunctions and eigenvalues in this context?

The eigenfunctions in this context are sinusoidal functions that satisfy the boundary conditions of the problem. The eigenvalues are related to the wavenumbers of these sinusoidal functions and are determined by the dimensions of the rectangular pipe.

Can the potential inside a rectangular pipe be time-dependent?

Yes, the potential inside a rectangular pipe can be time-dependent if the problem involves time-varying boundary conditions or sources. In such cases, the solution would involve solving the time-dependent form of Laplace's or Poisson's equation, often requiring additional methods like Fourier or Laplace transforms.

Similar threads

Boundary Conditions for an infinite rectangular pipe
Replies
4
Views
1K
Find potential within a pipe using Laplace's equation
Replies
18
Views
2K
Electrostatic Potential in a Box
Replies
1
Views
1K
I Where to find this uniqueness theorem of electrostatics?
Replies
27
Views
2K
Average value of the impulse as the parameters vary
Replies
14
Views
2K
Dielectric problem -- two line charges inside a dielectric cylinder
Replies
9
Views
2K
Electric potential inside a shell of charge
Replies
3
Views
2K
Electric Potential Inside an Infinite Rectangular Trough
Replies
1
Views
2K
Floating potential of a conductor in an electrical field
Replies
2
Views
2K
Calculate the electric potential inside the pipe
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top