So, I've solved many problems involving paralell sheets of conductors (finite, semi-infinite, and infinite) and also finite sheets at a given angle to eachother. I can post the results to these if it may be useful, but I'm more interested in sheets that are perpendicular.
Consider a semi-infinite sheet at
a\leq x < \infty , y = 0
and a perpenciular sheet
-\infty < y < \infty , x = 0
I'm struggling to find a conformal transformation that will map this problem onto some region (like two infinite paralell lines), from which I can more easily calculate the electrostatic potential and charge density on both sheets.