Conformal Transformation for Perpendicular Charged Sheets

[Morto]

So, I've solved many problems involving parallel sheets of conductors (finite, semi-infinite, and infinite) and also finite sheets at a given angle to each other. 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
<br /> a\leq x &lt; \infty , y = 0<br />
and a perpenciular sheet
<br /> -\infty &lt; y &lt; \infty , x = 0<br />

I'm struggling to find a conformal transformation that will map this problem onto some region (like two infinite parallel lines), from which I can more easily calculate the electrostatic potential and charge density on both sheets.

Any ideas?

 

[Mindscrape]

You ought to use an image charge, also known as the method of images.

 

[Morto]

How? That works with the symmetry of parallell plates, but there is no such symmetry here.

 

[Morto]

Can I consider the line of charge as a sum over an infinite number of point charges?