I've come to the result (using cylindrical coordinates)
#\sigma (z) = (-2q) / (pi*sqrt(R_0*(10R_0-6z)^3) )#
and i tried to get #Q# by integrating #2*pi*sqrt(R_0^2-z^2)*\sigma(z)dz# from #-R_0# to #R_0#.
But i can't solve that integral. I tried solving it numerically with arbitrary values and it...