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I was wondering what the electric field of a uniformly charged spherical cap is? Thereby I am referring to a spherical shell that was sliced into two pieces and we are only looking at one part of it. So in spherical coordinates it would mean that you would have a shell with radius $R$, it contains a full revolution of $2\pi$, but the polar angle does not go from $0$ to $\pi$ but rather from $0$ to some $\theta \in (0,\pi)$. And now I am looking for an equation that gives me the electric field for a given charge $Q$ on the shell.

It would be sufficient if somebody could give me the integral, that I have to evaluate!

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Are you talking about a spherical cap? –  udiboy Jul 22 '13 at 13:06
    
Yes, but I did not know the word –  Lipschitz Jul 22 '13 at 13:07
    
You can derive it just like you derived it for a complete spherical shell(atleast I derived it that way) by taking infinitesimally thin parallel rings on the spherical cap, then using the formula for the field on the axis of a ring. –  udiboy Jul 22 '13 at 13:10
    
could you tell me your result in order to check, as I have never done this before? –  Lipschitz Jul 22 '13 at 13:10
    
Nah, I'm too lazy to derive because I know it'll be brain wrecking just to do the integrals, :-P. If you post your derivation here, and then I would check it. –  udiboy Jul 22 '13 at 13:12
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