Question

PDE

Answer 1

Solving Laplace's Equation in Cylindrical:
\[\frac{1}{s} \frac{\partial}{\partial s}(s \frac{\partial V}{\partial s})+\frac{1}{s^2}\frac{\partial^2 V}{\partial \phi^2}+\frac{\partial^2 V}{\partial z^2}=0\]

Answer 2

Boundary conditions are a cylinder of length L, radius R.

Answer 3

\[V(R,\phi,0)=0=V(R,\phi,L)=V(R,\phi,z)\]

Answer 4

I assume you start with:
\[V(s,\phi,z)=S(s) \Phi (\phi) Z(z)\]
And separate the variables.