# Separation of variables, laplace equation

1. Sep 18, 2012

### merrypark3

1. The problem statement, all variables and given/known data
Two coaxial pipes(radius a) of the same diameter with a small gap between them are maintained at a potential difference V.

By separation of variables and fitting coefficient, guess the potential within the pipe, near the gap.

2. Relevant equations

3. The attempt at a solution

Cylindrical laplace equation.
$\frac{d^2 R}{dr ^2} + \frac{1}{r} \frac{dR}{dr} =0$

Wow can I handle the boundary condition at r=a? R=V/2 or R=-V/2 or R=0?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution