(Solved): An open spherical surface is defined by \( \mathrm{r}=2 \mathrm{~m}, 0 \leq \phi \leq 2 \pi \) and ...

An open spherical surface is defined by \( \mathrm{r}=2 \mathrm{~m}, 0 \leq \phi \leq 2 \pi \) and \( \pi / 2 \leq \theta \leq \pi \). The surface has a uniform charge density of \( \rho_{s}=4 \pi \varepsilon_{0} \). Find the electric field at origin. Hint: \( \int \sin (x) \cos (x)=-\frac{1}{4} \cos (2 x) \)