Voltage inbetween two angled plates?

[Ayol]

Potential between two angled plates?

I have a problem involving two angled plates

Diagram
http://imageshack.us/photo/my-images/841/paintzr.jpg/

L=10cm
d=1mm
$\phi$= 1°

Where I'm supposed to find the potential at any point between the plates. I recognize that I'm supposed to use the Laplace equation in cylindrical coordinates and that V is independent of z, but I end up with an equation that looks like:

0=1/ρ * ∂/∂ρ * (ρ * ∂V/∂ρ) + 1/ρ^2 * ∂^2v/∂ $\Phi$ ^2 (I think)

and I have no idea what I'm supposed to do with it. If someone could clarify that it would be nice.

Thanks in advance.

 

[member 553083]

The equation you have is correct. To solve it, you can separate the variables using the method of separation of variables. That is, assume that the solution has the form V(ρ,ϕ)=X(ρ)Y(ϕ). Substituting this form into the Laplace equation will yield two ordinary differential equations which can be solved separately. The general solution will be a linear combination of these two solutions.