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Homework Statement
A flat non conducting sheet lies in the x - y plane. The only charges in the system are on this sheet. In the half space above the sheet, z > 0, the potential is [itex]\varphi = \varphi _{0}e^{-kz}coskx[/itex]. Describe the charge distribution on the sheet.
Homework Equations
The Attempt at a Solution
We have that [itex]E = -\triangledown \varphi = (\varphi _{0}ke^{-kz}sinkx)\hat{i} + (\varphi _{0}ke^{-kz}coskx)\hat{k} [/itex] for z > 0 and [itex]\int_{S}E \cdot dA = 4\pi\int_{S} \sigma dA [/itex] but I'm not sure how to use it here; all I can see is that if I enclose a part of the sheet with a box then the only parts of the box with a net flux through them will be the top part of the box and the bottom part and for that case the total flux through the two together will be double the flux through the top part of the box and the field lines are not perpendicular to that top part. Not sure what to do with that.
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