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## Homework Equations

Continuous charged distribution $$|\vec E| = \frac{1}{4\pi\epsilon_0}\displaystyle \int\frac{\rho (r') dV}{r'^2}$$

## The Attempt at a Solution

I have followed the approach that cuts the sphere inti little rings of radius r each, starting by defining ##\sigma = Q/A = 2\pi rdrdz## then ##\lambda = \frac{Q}{L} = \rho drdz## then I tried the calculate the contribution of each ring ##\vec E_ring = \frac{\rho}{4\pi\epsilon_0}\displaystyle\int \frac{r(h-z)d\theta drdz}{(r^2 + (h-z)^2)^{\frac{3}{2}}}##

I have integrated this +help for wolfram alpha, and it yields to a wrong result, Can someone tell me where did I go wrong, Thanks !