• Support PF! Buy your school textbooks, materials and every day products Here!

Potential function, V

  • Thread starter satchmo05
  • Start date
  • #1
114
0

Homework Statement


Determine whether or not V = xy is the correct potential function for the geometry shown in the figure: http://img268.imageshack.us/img268/446/48401266.jpg [Broken] for the region 0 < x< 1 and 0 < y < 1. Why or why not? Assume that the region between the conducting plates has a relative permittivity of εr = 3.0.

Image for problem shown at this URL: http://img268.imageshack.us/img268/446/48401266.jpg [Broken]

Homework Equations


There are multiple equations for the potential function V. I do not know which one to use/how to use it.


The Attempt at a Solution


Don't really know to get started on this one. I would appreciate any help that you can provide. I just need to know how to get started. Thanks for the help!
 
Last edited by a moderator:

Answers and Replies

  • #2
1,860
0
You're testing whether or not the trial function obeys laplace's equation with the correct boundary conditions.
 
  • #3
114
0
Ah, that makes sense Mindscape. Thank you. Ok, so I have determined that del^2(V) does in fact equal 0. What does this tell me? Is it the correct potential function? By the uniqueness principle, can I conclude that V=xy is the only potential function for this design, given the boundary conditions?
 
  • #4
1,860
0
You also need to check the boundary conditions for V(x,y):

V(0,y)=0
V(x,0)=0
V(1,y)=1
V(x,1)=1
 
  • #5
114
0
I thought there were 2 criteria though for determining whether or not a given potential function is the solution the DiffEQ. I have already determined that the Laplacian holds true, what is the other?
 
  • #6
1,860
0
Well, if you're going to guess a solution, you'd better make sure that it satisfies the PDE to start with, and secondly that it satisfies the actual physical conditions when all is said and done.

V(x,y)=5x+7y

is that a solution? Why or why not?

Do you know how to find the solution from scratch if you had to? Maybe that would help you understand a little better.
 

Related Threads on Potential function, V

Replies
1
Views
487
Replies
3
Views
6K
Replies
8
Views
5K
Replies
2
Views
3K
  • Last Post
Replies
3
Views
664
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
478
Replies
3
Views
2K
Replies
7
Views
537
  • Last Post
Replies
4
Views
5K
Top