Consider a very thin flat plate positioned in the x-z plane. The plate is semi-infinite with an edge running along the z axis. The plate is held at potential V0. Using techniques from teh theory of complex variables a solution is determined to be:
V(x,y) = A/(2)1/2[(x2 + y2)1/2 - x]1/2 + V0
Where A is a constant.
Evaluate an expression for the y component of the electric field. Then carefully take limits for x > 0 and y approaching zero to show that the surface charge on the plate is given by:
s(x) = -A(epsilon0)/(x1/2)
The Attempt at a Solution
I've worked out a few other parts of this problem, but this part has me stumped. I take the derivative of V(x,y) with respect to y and that gives you the electric field for varying y, right? Then you would use Gauss' law, right? I can't seem to work it out though. My work is scanned and attached to this message.