(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A long copper pipe, with it's axis on the z axis, is cut in half and the two halves are insulated. One half is held at 0V, the other at 9V. Find the potential everywhere in space.

2. Relevant equations

[tex]\nabla^2V=0[/tex]

3. The attempt at a solution

Alright. This is a laplace's equation problem in two dimensions, since the potential should be independent of z because the pipe is infinite. Using separation of variables( [tex]V=R\Phi[/tex]) the solution to the two dimensional Laplace's EQ in cylindrical coordinates is:

[tex]R(r)=ar^k+br^-k[/tex]

[tex]\Phi(\phi)=A\sin(k\phi) + B\cos(k\phi)[/tex]

w/ [tex]V=R(r)\Phi(\phi)[/tex]

I am getting confused when I try to apply boundary conditions to this problem. Here is what I think the boundary conditions should be:

1) V should go to zero as r goes to infinity. (I don't think this is right, since the pipe is infinite, but I am not sure.)

2)V=0 for phi between 0 and pi, r=radius of pipe

3)V=9 for phi between 0 and 2pi, r=radius of pipe.

I can't figure out how to actually use these to eliminate any of the constants. Any help and hints would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Laplace's Equation in Cylindrical Coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**