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Homework Statement
Calculate the potential V(z), a height z above an infinite sheet with surface charge density [tex]\sigma[/tex] by integrating over the surface.
Homework Equations
[tex]V(z)=\frac{1}{4\pi\epsilon_0}\int_s{\frac{\sigma dA}{r}}[/tex]
The Attempt at a Solution
So [tex]V(z)=\frac{\sigma}{4\pi\epsilon_0}\int_{-\infty}^{\infty} \int_{-\infty}^{\infty}{\frac{dx dy}{\sqrt{x^2+y^2+z^2}}}
[/tex]
However, unless I am wrong, this integral does not converge.
We know the E-field due a infinite sheet is [tex]E=\frac{\sigma}{2\epsilon_0}[/tex], so the potential should be [tex]V=-\frac{z\sigma}{2\epsilon_0}[/tex], right? So where is the error?