I'm not sure whether to post this in the Mathematics or Physics forums, but I figure this problem is easily reduced to its transformation irrespective of the physics it describes.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a semi-infinite sheet of (infinitely thin) conductor charged to a potential [tex]V[/tex]. It is placed at a distance [tex]h[/tex] perpendicular to a perfectly screening bulk conductor (so the electric field is always perpendicular to the surface). See the attachment below. I want to investigate the charge density on the surface of both sheets. I'm struggling to determine the transformation that can describe the electrostatic field.

Now, I have calculated a similar problem with a semi-infinite conducting planeparalellto an infinite conducting plane at a distance [tex]h[/tex]

I have transformed it into the upper half-plane (so it looks like a capacitor), and I found the transformation

[tex]

z = h \left( \frac{w}{V} - \frac{1}{\pi} \left(1+ e^{-\frac{\pi w}{V}} \right) \right)

[/tex]

determines this electrostatic field. How can I transform my problem with perpendicular planes into something similar? Can I use this result, with another transformation? Any help would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Complex analysis of electrostatic problem

**Physics Forums | Science Articles, Homework Help, Discussion**