Can not find correct green's function

[t387]

Homework Statement

We have long wire with constant charge density that is put inside a grounded metal housing with a shape of cylindrical section (a ≤ r ≤ b and 0 ≤ ϕ ≤ α). We need to find potential inside the box.

2. Homework Equations
Δf=-(μ/ε0)*∂^2(r), where μ is linear charge density [As/m], ε0 is Vacuum permittivity, f is the potential (Δ is laplace operator) and ∂^2(r) is two-dimensional delta function.

f (a ≤ r ≤ b and 0 ≤ ϕ ≤ α) = 0

green's function for ΔG =∂^2(r),two dimensions and no boundary conditions:

G(r,r0)=(1/2*pi)*ln|r-r0|

The Attempt at a Solution

I am trying to solve the problem with green's function since it seems that solving this problem with separation of variables is too complicated.

 

[Dale]

I am trying to solve the problem with green's function

Please show what you have attempted so far

 

[Orodruin]

Apart from what @Dale said, can you argue for why you think this is more difficult to solve using orthogonal functions?