So I have to provide the expression of the eletric field generated by a sphere of radius R whose surface charge density is SIGMA and is constant, using ONLY coulomb's law (no Gauss theorem)
I take it the only way to find it is to decompose the sphere in elementary circle, find the eletric field created by these and then integrate somehow...
I guess I found the correct expression of the eletric field generated by a circle, but I don't know how I can find the eletric field generated by the whole sphere.

Any suggestion ? Perhaps I'm not doing it the right way, if that's the case, some hint would be welcome, thanks in advance.