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## Homework Statement

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 V

_{0}. Using techniques from teh theory of complex variables a solution is determined to be:

V(x,y) = A/(2)

^{1/2}[(x

^{2}+ y

^{2})

^{1/2}- x]

^{1/2}+ V

_{0}

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(epsilon

_{0})/(x

^{1/2})

## Homework Equations

## 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.

Thanks!

Andrew